Decimal Fractions and Decimals: practice solutions, Grade 4 – download the PDF

1 Reading a hundred grid ★★★

a. There are 46 shaded squares out of 100, so the fraction is \(\dfrac{46}{100}\).

b. 46 hundredths is written 0.46.

Answer: \(\dfrac{46}{100}=0.46\).

2 Fractions to decimals ★★★

a. 7 tenths: 0.7.

b. 9 hundredths needs a zero in the tenths place: 0.09.

c. 53 hundredths: 0.53.

d. 4 tenths: 0.4.

3 Decimals to fractions ★★★

a. 0.8 has one decimal place: \(\dfrac{8}{10}\).

b. 0.05 has two decimal places: \(\dfrac{5}{100}\).

c. \(\dfrac{62}{100}\).

d. \(\dfrac{3}{10}\).

4 Words to numbers ★★★

a. 0.7

b. 0.29

c. 4.6 (4 ones and 6 tenths)

d. 3.08 (3 ones, 0 tenths, 8 hundredths)

5 Value of each digit ★★★

The 5 is in the ones place, so it is worth 5. The 3 is in the tenths place, so it is worth 3 tenths, which is 0.3. The 7 is in the hundredths place, so it is worth 7 hundredths, which is 0.07.

Check: \(5+0.3+0.07=5.37\).

6 Reading a number line ★★★

Each step is one tenth, or 0.1. Point A is 2 steps from 0, so A = 0.2. Point B is 7 steps from 0, so B = 0.7.

7 Coins ★★★

3 dimes are \(3\times 0.10=0.30\) dollar. 5 pennies are \(5\times 0.01=0.05\) dollar. Together: \(0.30+0.05=0.35\).

Answer: Maya has $0.35.

8 Tenths to hundredths ★★★

a. Multiply top and bottom by 10: \(\dfrac{30}{100}\).

b. \(\dfrac{90}{100}\).

c. \(\dfrac{40}{100}\).

d. Divide top and bottom by 10: \(\dfrac{6}{10}\).

9 Adding with unlike denominators ★★★

a. \(\dfrac{3}{10}=\dfrac{30}{100}\), so \(\dfrac{30}{100}+\dfrac{4}{100}=\dfrac{34}{100}=0.34\).

b. \(\dfrac{5}{10}=\dfrac{50}{100}\), so \(\dfrac{50}{100}+\dfrac{27}{100}=\dfrac{77}{100}=0.77\).

10 Which is greater? ★★★

a. 0.4 = 0.40, and 40 hundredths is more than 38 hundredths, so \(0.4 > 0.38\).

b. 7 hundredths is less than 7 tenths: \(0.07 < 0.7\).

c. 1.3 = 1.30, and 125 hundredths is less than 130 hundredths: \(1.25 < 1.3\).

d. \(\dfrac{50}{100}=\dfrac{5}{10}\), so \(0.50 = 0.5\).

11 True or false? ★★★

a. True: \(\dfrac{5}{10}=\dfrac{50}{100}\).

b. True: 0.3 = 0.30 and 30 hundredths is more than 25 hundredths.

c. False: 0.1 = 0.10 and 10 hundredths is more than 9 hundredths.

d. False: \(\dfrac{6}{10}=0.6\). The decimal 0.06 is \(\dfrac{6}{100}\).

12 Putting in order ★★★

Write them in hundredths: 0.60, 0.06, 0.66, 0.16, 1.06. The only one with a 1 in the ones place is 1.06, so it is the greatest. Among the others: 6, 16, 60, 66 hundredths.

Answer: 0.06 < 0.16 < 0.6 < 0.66 < 1.06.

13 Saving for a book ★★★

Sam has \(2+0.30+0.04=2.34\) dollars. Compare: 2.34 is less than 2.43, so Sam does not have enough.

Missing: \(2.43-2.34=0.09\).

Answer: No, Sam is missing $0.09 (9 pennies).

14 Reading hundredths ★★★

a. Each step is 0.01. P is 2 steps after 0.3, so P = 0.32. Q is 7 steps after 0.3, so Q = 0.37.

b. Q is 3 steps from 0.4, and P is 8 steps from 0.4. So Q is closer to 0.4.

15 Ribbon ★★★

Rename the first length: \(\dfrac{3}{10}=\dfrac{30}{100}\).

Add: \(\dfrac{30}{100}+\dfrac{25}{100}=\dfrac{55}{100}\).

Answer: The pieces measure \(\dfrac{55}{100}\) meter, which is 0.55 meter, together.

16 Expanded form ★★★

a. 4 ones, 0 tenths and 7 hundredths: 4.07.

b. 12 ones, 3 tenths, 8 hundredths: 12.38.

c. \(6.52=6+\dfrac{5}{10}+\dfrac{2}{100}\).

17 Mystery number ★★★

A number between 0.4 and 0.5 has 4 in the tenths place. The hundredths digit is \(4+3=7\).

Answer: I am 0.47. Check: \(0.4 < 0.47 < 0.5\).

18 Find the mistake ★★★

Jaden is not right. He compared 35 and 4 as if the digits had no place values. The numbers must be compared in the same place: 0.4 = 0.40, which is 40 hundredths. Since 40 is greater than 35, \(0.4 > 0.35\).

19 Swim meet ★★★

Write the times in hundredths: Ava 12.45, Ben 12.50, Cora 12.05, Dev 12.54. All have 12 ones. Compare tenths: Cora has 0, Ava has 4, Ben has 5 and Dev has 5. Ben and Dev tie in tenths, and 50 < 54 in hundredths.

Answer: Cora (12.05), Ava (12.45), Ben (12.5), Dev (12.54). Cora wins.

20 At the store ★★★

Total: \(1.75+0.60=2.35\) dollars. Change: \(5.00-2.35=2.65\) dollars.

Check: \(2.35+2.65=5.00\).

Answer: The total is $2.35 and Omar gets $2.65 in change.

21 Three pieces of wire ★★★

Rename the tenths: \(\dfrac{4}{10}=\dfrac{40}{100}\) and \(\dfrac{6}{10}=\dfrac{60}{100}\).

Add: \(\dfrac{40}{100}+\dfrac{15}{100}+\dfrac{60}{100}=\dfrac{115}{100}=1.15\).

Answer: The total is 1.15 meters, which is more than 1 meter.

22 Closest to one half ★★★

Find the gaps. \(0.5-0.47=0.03\) and \(0.55-0.5=0.05\). Since 3 hundredths is less than 5 hundredths, 0.47 is closer.

Answer: 0.47 is closer to 0.5.