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Identifying Rational Numbers
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Identifying Rational Numbers
A rational number can be written as a fraction of two integers, with a non-zero denominator. Work through the questions and show your thinking where asked.
Recognising Rational Numbers
1.Which statement best describes a rational number?
- A number that can be written as a fraction of integers, with a non-zero denominator
- A number that must be larger than 1
- A number that can only be written as a whole number
- A number that has no decimal form
2.Select every rational number in this set: 4/5, 0.6, 35%, 2.125, √3.
Fractions and Decimals
3.For the fraction 5/8, name the numerator and the denominator.
4.Which option lists three fractions that are all rational numbers?
- 2/9, 7/11, 3/4
- 1/0, 5/6, 2/3
- √2, 4/7, 8/5
- 3/10, π, 9/2
5.Write each fraction in words: 2/3, 5/12, and 7/10.
6.In 0.84, what place value does each digit have: 8 and 4?
7.Write 0.4, 0.68, and 1.35 in words using place-value names.
8.Which statement about 0.272727… is correct?
- It is rational because its digits repeat in a pattern
- It is irrational because it has many decimal places
- It is not a number because it does not end
- It is rational only if it is rounded
Percentages and Equivalent Forms
9.How do you read 40% aloud?
- Forty percent
- Four tenths percent
- Four zero parts
- Forty whole numbers
10.Explain what the word 'percent' means.
11.Match each fraction to its equivalent decimal and percentage.
- 1/5
- 3/5
- 1/10
- 9/10
- 1/4
- 0.6 and 60%
- 0.25 and 25%
- 0.9 and 90%
- 0.2 and 20%
- 0.1 and 10%
Rational Numbers in Context
12.At a swimming carnival, Kahu's team swims 1.25 kilometres in a relay. Is 1.25 rational? Show one fraction equal to 1.25.
13.Keira records a race time of 18.50 seconds. Which parts of this value are rational numbers?
- 18, 0.50, and 18.50
- Only 18
- Only 0.50
- None of them
14.Hana finishes 3/4 of a swimming event. Shade a model to show 3/4.
Quick Check
15.True or false: every fraction with a non-zero denominator is a rational number.
TrueFalse
16.Write one rational number as a fraction, one as a terminating decimal, and one as a percentage.
17.Describe in your own words how you can tell that a number is rational.
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