## Engage NY Eureka Math 5th Grade Module 1 Mid Module Assessment Answer Key

### Eureka Math Grade 5 Module 1 Mid Module Assessment Task Answer Key

Question 1.

Compare using >, <, or =.

a. 0.4 0.127

Answer:- 0.4 0.127

b. 2 thousandths + 4 hundredths 0.036

Answer:- 2 thousandths + 4 hundredths 0.036

c. 2 tens 3 tenths 1 thousandth 20.31

Answer:- 2 tens 3 tenths 1 thousandth 20.31

d. 24 tenths 2.5

Answer:- 24 tenths 2.5

e. 4 × 10^{3} + 2 × 100 + 3 × \(\frac{1}{10}\) 4 × 1000 + 2 × 10^{2} + 3 × \(\frac{1}{10}\)

Answer:- 4 × 10^{3} + 2 × 100 + 3 × \(\frac{1}{10}\) 4 × 1000 + 2 × 10^{2} + 3 × \(\frac{1}{10}\)

f. 3 × \(\frac{1}{10}\) + 4 × \(\frac{1}{1000}\) 0.340

Answer:- 3 × \(\frac{1}{10}\) + 4 × \(\frac{1}{1000}\) 0.340

Question 2.

Model the number 8.88 on the place value chart.

Answer:-

a. Use words, numbers, and your model to explain why each of the digits has a different value. Be sure to use “ten times as large” and “one tenth as large” in your explanation.

Answer:- Even though there are 8 dicks in each column, they are different digits so they have

different values. 8 in ones place is 10 times as large as 8 in tenths place.

8 in hundredths place is 1/10 as large as 8 tenths.

b. Multiply 8.88 × 10^{4}. Explain the shift of the digits and the change in the value of each digit.

Answer:- 8.88 x 10^{4} = 88800

When multiplying by 10^{4} , each digit shifts 4 places to the left. 10^{4} equals 10 x 10 x 10 x 10 or

1000, So each digit becomes 10,000 times as large.

c. Divide the product from (b) by 10^{2}. Explain the shift of the digits and the change in the value of each digit.

Answer:- 88800 ÷ 10^{2} = 888

When dividing by 10^{2}, each digit shifts 2 places to the right, 10^{2 }equals 10 x 10 or 100, So each digit becomes 1/100 as large.

Question 3.

Rainfall collected in a rain gauge was found to be 2.3 cm when rounded to the nearest tenth of a centimeter.

a. Circle all the measurements below that could be the actual measurement of the rainfall.

Answer:-

b. Convert the rounded measurement to meters. Write an equation to show your work.

Answer:- 2.3 ÷ 10^{2} = 0.023

2.3 cm = 0.023m

Question 4.

Average annual rainfall totals for cities in New York are listed below.

Rochester | 0.97 meters |

Ithaca | 0.947 meters |

Saratoga Springs | 1.5 meters |

New York City | 1.268 meters |

a. Put the rainfall measurements in order from least to greatest. Write the smallest total rainfall in word form and expanded form.

Answer:- The rainfall measurements in order from least to greatest are

0.947m, 0.97m, 1.268m, 1.5m.

Nine hundred forty-seven thousandths. 9 x 1/10 + 4 x 1/100 + 7 x 1/1000

b. Round each of the rainfall totals to the nearest tenth.

Answer:- 0.97 m = 1.0m

0.947m = 0.9m

1.5m = 1.5m

1.268m = 1.3m

c. Imagine New York City’s rainfall is the same every year. How much rain would fall in 100 years?

Answer:- 1.268 m x 100 = 126.8m

126.8 m would fall in 100 years

d. Write an equation using an exponent that would express the 100-year total rainfall. Explain how the digits have shifted position and why.

Answer:- 1.268m x 10^{2} = 126.8m. Each digit shifts 2 places to the left when multiplying by 10^{2}. The value of each digit becomes 100 times as large.

1 x 100 = 100

0.2 x 100 = 20

0.06 x 100 = 6

0.008 x 100 = 0.8