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Spectrum Math Grade 5 Chapter 2 Pretest Answers Key
Check What You Know
Understanding Place Value
What is the value of the underlined digit?
Question 1.
a. 4,332
_________________
Answer:
300
Explanation:
We know that,
The place value is the value of a digit according to its position in the number such as,
ones, tens, hundreds, thousands, and so on.
So, the place value of 3 in 4,332 is 3 hundred or 300.
b. 52,321
_________________
Answer:
2,000
Explanation:
We know that,
The place value is the value of a digit according to its position in the number such as,
ones, tens, hundreds, thousands, and so on.
So, the place value of 2 in 52,321 is 2 thousand or 2,000.
Write the digit that is in the given place value.
Question 2.
30.146 – hundredth
_________________
Answer:
4
Explanation:
We know that, every digit in a number has a place value on the basis of its position in the number.
But in decimal numbers, the first digit after the decimal represents the tenths place, next digit represents the hundredths place and so on.
So, 4 is in the hundredths place of the given number 30.146.
b. 1,325.12 – thousand
_________________
Answer:
1
Explanation:
We know that the place value is the value of a digit,
Face value is the actual value of the digit,
whereas place value is the position of a digit in a number.
From the given number 1,325.12, 1 is in the thousands place.
So, based on the above given chart,
the place value of 1 in 1,325.12 is written as 1 thousands or 1,000.
Question 3.
a. 1.325 – tenth
Answer:
3
Explanation:
We know that, every digit in a number has a place value on the basis of its position in the number.
But in decimal numbers, the first digit after the decimal represents the tenths place, next digit represents the hundredths place and so on.
So, 3 is in the tenths place of the given number 1.325.
b. 731.045 – one
Answer:
1
Explanation:
We know that the place value is the value of a digit,
Face value is the actual value of the digit,
whereas place value is the position of a digit in a number.
From the given number 731.045, 1 is in the ones place.
So, based on the above given chart,
the place value of 1 in 731.045 is written as 1 ones or 1.
Convert each power of ten to a standard number.
Question 4.
a. 104 _______
Answer:
10,000
Explanation:
An exponent is a number that shows how many times a base number is to be used in multiplication.
A power of ten is an exponent where the base number is always 10.
104 = 10 × 10 × 10 × 10 = 10,000
So, 104 is written as 10,000.
b. 106 _______
Answer:
1,000,000
Explanation:
An exponent is a number that shows how many times a base number is to be used in multiplication.
A power of ten is an exponent where the base number is always 10.
106 = 10 × 10 × 10 × 10 x 10 x 10 = 1000,000
So, 106 is written as 1000,000.
Multiply or divide by the given power of ten.
Question 5.
a. 8.75 × 1,000 _______
Answer:
8,750
Explanation:
We know that,
when a number is multiplied by a multiple of 10,
the number of zeros and decimals in the product will vary based on the value of the multiple of 10 that is used and the decimal in the product moves to the right and zeros are added to the left of the decimal when needed.
So, 8.75 × 1,000 = 8,750
b. 7,643 ÷ 100 _____
Answer:
76.43
Explanation:
We know that,
When a number is divided by a multiple of 10,
the number of zeros and decimals in the quotient will vary based on the value of the multiple of 10 that is used and the decimal in the quotient moves to the left and zeros are added to the right of the decimal when needed.
So, 7643 ÷ 100 = 76.43
Question 6.
a. 45.67 × 1,000 ________
Answer:
45,670
Explanation:
We know that,
when a number is multiplied by a multiple of 10,
the number of zeros and decimals in the product will vary based on the value of the multiple of 10 that is used and the decimal in the product moves to the right and zeros are added to the left of the decimal when needed.
So, 45.67 × 1,000 = 45,670
b. 34,981 ÷ 1,000 _____
Answer:
34.981
Explanation:
We know that,
When a number is divided by a multiple of 10,
the number of zeros and decimals in the quotient will vary based on the value of the multiple of 10 that is used and the decimal in the quotient moves to the left and zeros are added to the right of the decimal when needed.
So, 34,981 ÷ 1,000 = 34.981
Write the numbers in expanded form.
Question 7.
a. 592,682
_________________
Answer:
500,000 + 90,000 + 2,000 + 600 + 80 + 2
Explanation:
We know that,
Expanded form is a method to show the sum of values of each digit of a number.
In expanded form we separate a number into each of its parts using place value.
Given,
592,682 = 500,000 + 90,000 + 2,000 + 600 + 80 + 2
5 in hundred thousands place is written as 5 x 100,000 = 500,000
9 in ten thousands place is written as 9 x 10,000 = 90, 000
2 in thousands place is written as 2 x 1000 = 2,000
6 in hundreds places is written as 6 x 100 = 600.
8 in tens place is written as 8 x 10 = 80.
2 in ones place is written as 2 x 1 = 2.
So, the sum of500,000 + 90,000 + 2,000 + 600 + 80 + 2 = 592,682
b. 78.364
_________________
Answer:
70 + 8 + 0.3 +0.06 + 0.004
Explanation:
To write a decimal numbers in expanded form,
we need to break down each digit according to its place value.
First start with the whole numbers by identifying the place values of numbers as ones, tens, hundreds, thousands, and so on.
Then, move on to the decimal part as tenths, hundredths, and thousandths places.
So, 78.364 is written as 70 + 8 + 0.3 +0.06 + 0.004
Compare each pair of decimals using <, >, or =.
Question 8.
a. 6.203 ____ 6.214
Answer:
6.203 < 6.214
Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenth place are same.
So, move to the hundredths place, the numbers are different.
Hence, 6.203 < 6.214 or 6.203 is less than 6.214.
b. 2.4 _____ 2.400
Answer:
2.4 = 2.400
Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenth place are same.
There is no value for zero in the decimal numbers at the last.
So, 2.4 = 2.400
c. 48.28 ____ 46.281
Answer:
48.28 > 46.281
Explanation:
Compare the whole number part first.
If the numbers are same in tens place, then go to the next ones place.
So, 48.28 > 46.281 or 48.28 is greater than 46.281.
Question 9.
a. 72.355 _____ 72.335
Answer:
72.355 > 72.335
Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenth place are same.
Then move to the hundredths place.
So, 72.355 > 72.335 or 72.355 is greater than 72.335.
b. 5.76 ____ 50.76
Answer:
5.76 < 50.76
Explanation:
Compare the whole number part first.
The numbers in tens place are different.
So, 5.76 < 50.76 or 5.76 is less than 50.76.
c. 9.763 ____ 9.673
Answer:
9.763 > 9.673
Explanation:
Compare the whole number part first.
The numbers in tens place are same, then go to the ones place.
So, 9.763 > 9.673 or 9.763 is greater than 9.673.
Order the decimals from least to greatest.
Question 10.
72.5, 73.943, 72.1, 73.77
_________________
Answer:
72.1, 72.5, 73.77, 73.943
Explanation:
Given,
72.5, 73.943, 72.1, 73.77
To order a group of decimals, line up the decimal points.
72.5,
73.943,
72.1,
73.77
All the ones are the same.
73.943 and 73.77 have the different tenths digit.
So, 73.943 is greater than 73.77.
In the other two numbers when we compare the tenth place 72.5 is greater than 72.1.
Know list from least to greatest:
72.1, 72.5, 73.77, 73.943
Question 11.
43.2, 43.219, 42.1, 42.59
_________________
Answer:
42.1, 42.59, 43.2, 43.219
Explanation:
Given,
43.2, 43.219, 42.1, 42.59
To order a group of decimals, line up the decimal points.
43.2,
43.219,
42.1,
42.59
All the ones are the same.
43.219 and 43.2 have the same tenths digit, but hundredths are different.
So, 43.219 is greater than 43.2
In the other two numbers when we compare the tenth place 42.59 is greater than 42.1
Know list from least to greatest:
42.1, 42.59, 43.2, 43.219
Question 12.
38.507, 38.4, 38.23, 39.5
_________________
Answer:
38.23, 38.4, 38.507, 39.5
Explanation:
Given,
38.507, 38.4, 38.23, 39.5
To order a group of decimals, line up the decimal points.
38.507,
38.4,
38.23,
39.5
All the ones are the same.
39.5 and 38.507 have the same tens digit, but ones digits are different.
So, 39.5 is greater than 38.507
In the other two numbers when we compare the tenth place 38.4 is greater than 38.23
Know list from least to greatest:
38.23, 38.4, 38.507, 39.5
Question 13.
71.743, 71.3, 72.43, 72.5
Answer:
71.3, 71.743, 72.43, 72.5
Explanation:
Given,
71.743, 71.3, 72.43, 72.5
To order a group of decimals, line up the decimal points.
71.743,
71.3,
72.43,
72.5
All the ones are the same.
72.5 and 72.43 have the different tenths digit.
So, 72.5 is greater than 72.43
In the other two numbers when we compare the tenth place 71.743 is greater than 71.3
Know list from least to greatest:
71.3, 71.743, 72.43, 72.5
Round each number to the indicated place.
Question 14.
a. 3.171 – tenths
Answer:
3.2
Explanation:
Round 3.171 to the nearest tenth.
Look at the hundredths digit.
7 is greater than 5, so round 1 to 2 in the tenths place.
Therefore, 3.171 is rounded to the nearest tenth as 3.2
b. 2.253 – ones
Answer:
2
Explanation:
Round 2.253 to the nearest ones
Look at the tenths digit.
2 is less than 5, so keep the same number in the ones place.
Therefore, 2.253 is rounded to 2.
c. 5.126 – hundredths
Answer:
5.13
Explanation:
Round 5.126 to the nearest hundredth.
Look at the thousandths digit.
6 is greater than 5, so round 2 to 3 in the hundredth place.
Therefore, 5.126 is rounded to the nearest hundredth as 5.13.
Question 15.
a. 64.967 – ones
Answer:
65
Explanation:
Round 64.967 to the nearest ones
Look at the tenths digit.
9 is greater than 5, so round the 4 to 5 in ones place.
Therefore, 64.967 is rounded to 65.
b. 9.432 – tenths
Answer:
9.4
Explanation:
Round 9.432 to the nearest tenth.
Look at the hundredths digit.
3 is less than 5, so the number in the tenths place remains same.
Therefore, 9.432 is rounded to the nearest tenth as 9.4
c. 1.225 – hundredths
Answer:
1.23
Explanation:
Round 1.225 to the nearest hundredth.
Look at the thousandths digit.
5 is greater than or equal to 5, so round 2 to 3 in the hundredth place.
Therefore, 1.225 is rounded to the nearest hundredth as 1.23.