Math Detours · Grade 5 · Connections · 4

Won by a hundredth of a second

Races are timed to hundredths. Read the stopwatch, order the finishers, and see how far a sprinter runs in 0.01 s.

Name ____________________Date ____________

Tonight's idea

In a sprint, whole seconds are not enough. Several runners can finish inside the same second. So races are timed in smaller pieces.

Cut one second into 10 equal parts. Each part is a tenth, written 0.1 s. Cut each tenth into 10 again. Now there are 100 parts in a second. Each is a hundredth, written 0.01 s. That is far quicker than a blink.

1 0 . 2 4 seconds tenths hundredths 10.1 10.2 10.3 Cal 10.19 Bea 10.24 Ali 10.30 ← faster  ·  each small step is 0.01 s  ·  slower →
Left: how to read a race time. Right: three finishers on a number line cut into hundredths.

A time of 10.24 s means 10 seconds, 2 tenths and 4 hundredths. The lowest time wins.

To compare times, look at the seconds first, then the tenths, then the hundredths.

Some times are written with one digit after the point, like 10.3. Fill the empty place with a zero: 10.3 is 10.30. Three tenths is the same as thirty hundredths, so nothing has changed.

Watch one: Ali 10.3, Bea 10.24, Cal 10.19

Write Ali's time as 10.30. All three have 10 seconds, so look at the tenths. Cal has 1 tenth. Bea has 2. Ali has 3. The order is Cal, Bea, Ali.

How close was it? Take the winner's time from Bea's.

\[10.24 - 10.19 = 0.05\]

Cal won by 5 hundredths of a second. Notice that 10.3 looked small, but it was the slowest time.

Your turn

  1. A stopwatch shows 12.47 s. (a) What is the 4 worth? (b) What is the 7 worth? (c) How many hundredths of a second are there in 0.5 s?
  2. Four runners finish in 11.4 s, 11.08 s, 11.36 s and 11.3 s. Put the times in order, winner first.
  3. The winner of a race took 10.92 s. Second place took 11.05 s. (a) By how much did the winner win? (b) Third place was 0.2 s behind second place. What was the third time?
  4. A sprinter runs 100 m in exactly 10 s. Pretend her speed is steady. (a) How far does she run in 1 s? (b) How far in 0.1 s? (c) How far in 0.01 s? Answer in centimetres. (d) She wins by 0.03 s. About how far ahead is she at the finish?

Stretch: in the pool

A swimmer swims 50 m in 25 s at a steady speed. How far does she swim in 0.01 s? She touches the wall 0.04 s after the winner. About how far behind was she?

Answers

  1. (a) 4 tenths of a second, or 0.4 s. (b) 7 hundredths of a second, or 0.07 s. (c) 50, because 0.5 is 0.50.
  2. Write them all with two places: 11.40, 11.08, 11.36, 11.30. The order is 11.08, 11.3, 11.36, 11.4.
  3. (a) \(11.05 - 10.92 = 0.13\) s. Count up to check: 10.92 to 11.00 is 0.08, and 0.05 more makes 0.13. (b) \(11.05 + 0.20 = 11.25\) s.
  4. (a) \(100 \div 10 = 10\) m. (b) A tenth of that: 1 m. (c) A tenth again: 0.1 m, which is 10 cm. (d) \(3 \times 10 = 30\) cm, about the length of a ruler.

Stretch. In 1 s she swims \(50 \div 25 = 2\) m, which is 200 cm. In 0.01 s she swims \(200 \div 100 = 2\) cm. In 0.04 s that is \(4 \times 2 = 8\) cm. She lost by about the width of a hand.

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