NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Equivalent fractions and decimals

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A sports equipment supplier in Perth is allocating 53 identical tennis balls and 49 identical netballs to schools. What is the exact decimal representation of the fraction of netballs in the total allocation?

Express your answer as a recurring decimal using correct notation.

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Half in three forms. 1/2 = 0.5 = 50%. The whole is divided into two equal parts.1 of 2 equal parts
1/2 = 0.5 = 50%. The whole is divided into two equal parts.
Common denominators as equal strips. The first strip selects 4/12 = 1/3; the second selects 3/12 = 1/4. The result selects 7/12. Every strip represents the same whole.1/31/47/124/12 + 3/12 = 7/12
The first strip selects 4/12 = 1/3; the second selects 3/12 = 1/4. The result selects 7/12. Every strip represents the same whole.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The total number of balls is the sum of tennis balls and netballs: 53 + 49 = 102.
  2. The fraction of netballs is 49 out of 102, written as 49/102.
  3. To convert the fraction to a decimal, divide 49 by 102 using long division.
  4. 49 ÷ 102: 102 goes into 490 four times (102 × 4 = 408), remainder 82.
  5. Bring down a 0 to make 820. 102 goes into 820 eight times (102 × 8 = 816), remainder 4.
  6. Bring down a 0 to make 40. 102 goes into 40 zero times. Write 0 and bring down another 0 to make 400.
  7. 102 goes into 400 three times (102 × 3 = 306), remainder 94.
  8. Bring down a 0 to make 940. 102 goes into 940 nine times (102 × 9 = 918), remainder 22.
  9. Bring down a 0 to make 220. 102 goes into 220 two times (102 × 2 = 204), remainder 16.
  10. Bring down a 0 to make 160. 102 goes into 160 one time (102 × 1 = 102), remainder 58.
  11. Bring down a 0 to make 580. 102 goes into 580 five times (102 × 5 = 510), remainder 70.
  12. The decimal repeats from earlier remainders. The recurring pattern is found to be 0.(4803921568627450980392156862745098), but the full cycle is long. The decimal is 0.4803921568627450980392156862745098... and the repeating block is 16 digits long. The correct recurring decimal notation is 0.480392156862745098 with a bar over the full repeating sequence. However, for simplicity and standard form, the decimal is 0.480392156862745098... and the repeating block is 480392156862745098. The exact recurring decimal is 0.480392156862745098 with a bar over the entire repeating part. The correct notation is 0.(480392156862745098).

Reference answer: 0.(480392156862745098)

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