This handy Spectrum Math Grade 7 Answer Key Chapter 2 Lesson 2.8 Converting Rational Numbers Using Division provides detailed answers for the workbook questions.
Spectrum Math Grade 7 Chapter 2 Lesson 2.8 Converting Rational Numbers Using Division Answers Key
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat.
Terminating
Repeating
Use long division to change each rational number into a decimal. Then, circle to indicate if each is terminating (T) or repeating (R).
Question 1.
a. \(\frac{1}{4}\) = _____ T or R
Answer: 0.25, T
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 1 by 4, we will get terminating decimal 0.25
Therefore, \(\frac{1}{4}\) = 0.25
b. 2\(\frac{3}{5}\) = _____ T or R
Answer: 2.6, T
Convert mixed fraction into improper fraction to maker calculations easy.
2\(\frac{3}{5}\) = \(\frac{13}{5}\)
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 13 by 5, we will get terminating decimal 2.6
Therefore, 2\(\frac{3}{5}\) = 2.6
c. \(\frac{5}{8}\) = _____ T or R
Answer: 0.625, T
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 5 by 8, we will get terminating decimal 0.625
Therefore, \(\frac{5}{8}\)= 0.625
Question 2.
a. \(\frac{3}{5}\) = _____ T or R
Answer: 0.6, T
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 3 by 5, we will get terminating decimal 0.6
Therefore, \(\frac{3}{5}\) = 0.6
b. \(\frac{7}{200}\) = _____ T or R
Answer: 0.035, T
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 7 by 200, we will get terminating decimal 0.035
Therefore, \(\frac{7}{200}\) = 0.035
c. \(\frac{8}{33}\) = _____ T or R
Answer: 0.242424, R
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 7 by 200, we will get repeating decimal 0.242424, so a line was indicated above 24.
Therefore, \(\frac{8}{33}\) = 0.2424
Question 3.
a. \(\frac{6}{11}\) = _____ T or R
Answer: 0.545454, R
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 6 by 11, we will get repeating decimal 0.545454, so a line was indicated above 54.
Therefore, \(\frac{6}{11}\) = 0.545454
b. \(\frac{7}{50}\) = _____ T or R
Answer: 0.14, T
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 7 by 50, we will get terminating decimal 0.14
Therefore, \(\frac{7}{50}\) = 0.14
c. 4\(\frac{17}{125}\) = _____ T or R
Answer: 4.136, T
Convert the mixed fraction into improper fraction to make the calculations easy.
4\(\frac{17}{125}\) = \(\frac{517}{125}\)
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 517 by 125, we will get terminating decimal 4.136
Therefore, 4\(\frac{17}{125}\) = 4.136
Question 4.
a. \(\frac{7}{20}\) = _____ T or R
Answer: 0.35, T
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 7 by 20, we will get terminating decimal 0.35
Therefore, \(\frac{7}{20}\) = 0.35
b. \(\frac{1}{111}\) = _____ T or R
Answer: 0.009009, R
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 1 by 111, we will get repeating decimal 0.009009, so a line was indicated above 009.
Therefore, \(\frac{1}{111}\) = 0.009009
c. \(\frac{1}{125}\) = _____ T or R
Answer: 0.008, T
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 1 by 125, we will get terminating decimal 0.008
Therefore, \(\frac{1}{125}\) = 0.008
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat.
Repeating
Add a line above digits to show they repeat.
Terminating
Change each rational number into a decimal using long division. Place a line above any digits which repeat.
Question 1.
a. \(\frac{4}{10}\) = ____
Answer: 0.4
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 4 by 10, we will get terminating decimal 0.4
Therefore, \(\frac{4}{10}\) = 0.4
b. \(\frac{2}{3}\) = ____
Answer: 0.6666
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 2 by 3, we will get repeating decimal 0.6666, so a line was indicated above 6.
Therefore, \(\frac{2}{3}\) = 0.6666
c. \(\frac{5}{10}\) = ____
Answer: 0.5
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 5 by 10, we will get terminating decimal 0.5
Therefore, \(\frac{5}{10}\) = 0.5
Question 2.
a. \(\frac{3}{8}\) = ____
Answer: 0.375
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 3 by 8, we will get terminating decimal 0.375
Therefore, \(\frac{3}{8}\) = 0.375
b. \(\frac{2}{11}\) = ____
Answer: 0.181818
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 2 by 11, we will get repeating decimal 0.181818, so a line was indicated above 18.
Therefore, \(\frac{2}{11}\) = 0.181818
c. \(\frac{3}{7}\) = ____
Answer: 0.428571428571
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 3 by 7, we will get repeating decimal 0.428571428571, so a line was indicated above 428571.
Therefore, \(\frac{3}{7}\) = 0.428571428571
Question 3.
a. \(\frac{1}{6}\) = ____
Answer: 0.1666
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 1 by 6, we will get repeating decimal 0.1666, so a line was indicated above 6.
Therefore, \(\frac{1}{6}\) = 0.1666
b. \(\frac{4}{6}\) = ____
Answer: 0.6666
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 4 by 6, we will get repeating decimal 0.666, so a line was indicated above 6.
Therefore, \(\frac{4}{6}\) = 0.6666
c. \(\frac{11}{22}\) = ____
Answer: 0.5
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 11 by 22, we will get terminating decimal 0.5
Therefore, \(\frac{11}{22}\) = 0.5
Question 4.
a. \(\frac{1}{4}\) = ____
Answer: 0.25
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 1 by 4, we will get terminating decimal 0.25
Therefore, \(\frac{1}{4}\) = 0.25
b. \(\frac{8}{10}\) = ____
Answer: 0.8
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 8 by 10, we will get terminating decimal 0.8
Therefore, \(\frac{8}{10}\) = 0.8
c. \(\frac{3}{10}\) = ____
Answer: 0.3
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 3 by 10, we will get terminating decimal 0.3
Therefore, \(\frac{3}{10}\) = 0.3
Question 5.
a. \(\frac{6}{10}\) = ____
Answer: 0.6
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 6 by 10, we will get terminating decimal 0.6
Therefore, \(\frac{6}{10}\) = 0.6
b. \(\frac{5}{7}\) = ____
Answer: 0.714285714285
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 5 by 7, we will get repeating decimal 0.714285714285, so a line was indicated above 714285.
Therefore, \(\frac{5}{7}\) = 0.714285714285
c. \(\frac{2}{11}\) = ____
Answer: 0.1818
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 2 by 11, we will get repeating decimal 0.181818, so a line was indicated above 18.
Therefore, \(\frac{2}{11}\) = 0.181818
Question 6.
a. \(\frac{1}{10}\) = ____
Answer: 0.1
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 1 by 10, we will get terminating decimal 0.1
Therefore, \(\frac{1}{10}\) = 0.1
b. \(\frac{5}{6}\) = ____
Answer: 0.8333
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 5 by 6, we will get repeating decimal 0.833, so a line was indicated above 3.
Therefore, \(\frac{5}{6}\) = 0.8333
c. \(\frac{3}{6}\) = ____
Answer: 0.5
Rational numbers can be converted into decimals using long division. All fractions will be turned into decimals that either terminate or repeat. Repeating decimals can be given as a same pattern of numbers will get when we perform division. A line will be placed above the digits which are repeating.
Here, If we divide 3 by 6, we will get terminating decimal 0.5
Therefore, \(\frac{3}{6}\) = 0.5