Place Value and Decimals: math practice, Grade 5 – download the PDF

1 Value of each digit ★★★

In the number \(482.317\), give the value of (a) the 8, (b) the 3, (c) the 1, (d) the 7.

2 Ten times and one tenth ★★★

Fill in each blank.

1. \(7 = 10 \times\) ___
2. \(0.08\) is 10 times as much as ___
3. \(0.4\) is \(\dfrac{1}{10}\) of ___
4. \(600\) is \(\dfrac{1}{10}\) of ___

3 Powers of ten ★★★

(a) Write each number as a power of 10: \(100\), \(100{,}000\), \(10\).

(b) Write in standard form: \(10^4\) and \(10^6\).

4 Words to numbers ★★★

Write each number in standard form.

1. nine and four hundred twenty-seven thousandths
2. sixty-three hundredths
3. five thousandths
4. twelve and eight tenths

5 Numbers to words ★★★

Write each number in words: (a) \(30.205\) (b) \(0.09\) (c) \(7.018\).

6 Greater, less or equal ★★★

Write \(<\), \(>\) or \(=\) in each blank.

1. \(0.8\) ___ \(0.79\)
2. \(3.45\) ___ \(3.450\)
3. \(0.099\) ___ \(0.1\)
4. \(12.06\) ___ \(12.6\)

7 Round to the nearest tenth ★★★

Round each number to the nearest tenth: \(6.37\), \(0.82\), \(2.04\), \(9.96\).

8 Expanded form ★★★

1. Write \(73.406\) in expanded form.
2. Write \(2 \times 100 + 5 \times 0.1 + 9 \times 0.001\) in standard form.
3. Write \(6 \times 1 + 8 \times \dfrac{1}{10} + 3 \times \dfrac{1}{100}\) in standard form.

9 Order from least to greatest ★★★

Order these numbers from least to greatest: \(4.052\), \(4.25\), \(4.5\), \(4.205\), \(4.025\).

10 Reading a number line ★★★

The number line shows points \(A\), \(B\) and \(C\). Each small tick is one hundredth.

1. Write the value of each point.
2. Round each value to the nearest tenth.

11 Multiplying by powers of 10 ★★★

Calculate: (a) \(3.42 \times 10\) (b) \(0.068 \times 100\) (c) \(5.7 \times 1{,}000\) (d) \(0.4 \times 10^2\) (e) \(12.5 \times 10^3\).

12 Dividing by powers of 10 ★★★

Calculate: (a) \(4.5 \div 10\) (b) \(62 \div 100\) (c) \(8.3 \div 1{,}000\) (d) \(730 \div 10^2\) (e) \(0.9 \div 10^2\).

13 Sprint times ★★★

Four runners finished the 100-meter dash in these times (in seconds): Ava \(11.48\), Ben \(11.4\), Cleo \(11.52\), Dev \(11.399\). Who won? List the runners from first to last place.

14 Rounding to different places ★★★

Round \(7.4968\) to (a) the nearest whole number, (b) the nearest tenth, (c) the nearest hundredth, (d) the nearest thousandth.

15 Metric conversions ★★★

1. A rope is \(3.5\) meters long. How many centimeters is that?
2. A bottle holds \(2{,}450\) milliliters. How many liters is that?
3. A \(7.2\)-kilogram bag of rice is shared equally into 100 packets. How much rice is in one packet, in kilograms and in grams?

16 True or false? ★★★

Decide if each statement is true or false, and explain.

1. \(0.30 > 0.3\)
2. \(5.6 \times 10^2 = 5{,}600\)
3. \(0.07\) is 10 times as much as \(0.007\).
4. \(3.09 > 3.1\)

17 Mystery number ★★★

Find my number. It has 2 digits before the decimal point and 3 after it. The tens digit is 2. The ones digit is 7. The tenths digit is 3 less than the ones digit. The hundredths digit is 0. The thousandths digit is 1 more than the tenths digit.

1. What is my number?
2. Write it in words.
3. Round it to the nearest tenth.
4. What do you get when you multiply it by \(10^2\)?

18 Find the mistake ★★★

Leo wrote: “\(2.5 \times 10^3 = 2.5000\)” and “\(0.45 \div 10 = 4.5\)”. Explain each mistake and give the correct answers.

19 Digits and numbers in between ★★★

1. Use the digits 3, 0, 5 and 7 exactly once each to fill the pattern ___.___ ___ ___. What is the greatest number you can make? The least?
2. Write three decimals between \(0.47\) and \(0.48\).
3. How many numbers with exactly three decimal places lie strictly between \(0.47\) and \(0.48\)?

20 Under the microscope ★★★

A bacterium is \(0.0042\) cm long. A microscope magnifies by \(10^3\) and another one by \(10^2\).

1. How long does it look with the \(10^3\) microscope?
2. How long with the \(10^2\) microscope?
3. How many times longer is the first image than the second?

21 Capsule factory ★★★

A factory puts \(4.6\) grams of a vitamin powder in each capsule. A batch contains \(10^3\) capsules.

1. How many grams of powder are in one batch? How many kilograms?
2. The powder of the batch is poured equally into \(10^2\) jars. How many grams are in each jar?

22 Comparing places ★★★

In the number \(555.555\):

1. The 5 in the hundreds place is how many times the value of the 5 in the tens place?
2. The 5 in the tens place is what fraction of the 5 in the hundreds place?
3. How many times the value of the 5 in the hundredths place is the 5 in the hundreds place? Write the answer as a power of 10.