A billion heartbeats
Tonight's idea
Press two fingers on the inside of your wrist, just below the thumb. Each small push is one heartbeat. A resting heart beats about 80 times a minute. Count yours for one minute and see.
Eighty does not sound like much. But your heart never stops, so the beats pile up. To find how many, multiply up through the units of time.
An hour is 60 minutes: \(80 \times 60 = 4{,}800\) beats. A day is 24 hours: \(4{,}800 \times 24 = 115{,}200\). A year is 365 days: \(115{,}200 \times 365 = 42{,}048{,}000\).
That is about 42 million beats a year. A million is a thousand thousands. The next big name is a billion: a thousand millions, written 1,000,000,000.
Bigger unit of time, so multiply: × 60 for an hour, × 24 for a day, × 365 for a year.
Watch one: ten years old
How many beats in ten years? One year is 42,048,000. Multiply by 10: every digit moves one place to the left, giving 420,480,000.
Read it in groups of three from the right: 420 million, 480 thousand. A ten-year-old heart has beaten about 420 million times.
Check by rounding: 40 million × 10 is 400 million. That is close, so the answer is sensible. (Leap years add a few days. We leave them out.)
Your turn
- A heart beats 80 times a minute. How many beats is that in (a) 10 minutes, (b) one hour, (c) a film that lasts 2 hours?
- A mouse has a much faster heart. Suppose it beats 500 times a minute. How many beats is that in (a) one hour, (b) one day?
- At 80 beats a minute, a heart beats 115,200 times a day. (a) How many beats in 8 days? (b) How many in 9 days? (c) On which day does the count pass one million?
- A billion is 1,000 million. (a) Round one year to 40 million beats. About how many years does a billion beats take? (b) Now use 42 million. Work out \(42 \times 23\) and \(42 \times 24\). How old is a person when the count passes a billion?
Stretch: the elephant and the mouse
An elephant's heart beats about 30 times a minute. An elephant can live about 60 years. A mouse's heart beats about 600 times a minute. A mouse may live 3 years. Which has more heartbeats in its life? Try not to multiply everything out.
Answers
- (a) \(80 \times 10 = 800\). (b) \(80 \times 60 = 4{,}800\). (c) \(4{,}800 \times 2 = 9{,}600\).
- (a) \(500 \times 60 = 30{,}000\). (b) \(30{,}000 \times 24 = 720{,}000\).
- (a) \(115{,}200 \times 8 = 921{,}600\). (b) \(115{,}200 \times 9 = 1{,}036{,}800\). (c) After 8 days the count is under a million and after 9 days it is over. So it passes one million during day 9.
- (a) \(1{,}000 \div 40 = 25\), so about 25 years. (b) \(42 \times 23 = 966\) and \(42 \times 24 = 1{,}008\). After 23 years the count is 966 million. After 24 years it is 1,008 million. So it passes a billion during the 24th year of life, when the person is 23 years old.
Stretch. They are equal. The mouse's heart is 20 times as fast, because \(30 \times 20 = 600\). The elephant lives 20 times as long, because \(3 \times 20 = 60\). The two cancel out. Each gets \(30 \times 60 \times 24 \times 365 \times 60 = 946{,}080{,}000\) beats, a little under a billion.