Math

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Please explain how I write this into a decimal and as a fraction in simplest form:

94.6%

Thanks!

• Math -

For a decimal, move the decimal point two places to the left or divide by 100.

94.6% = 0.946

Reading the decimal in words we get --
nine hundred forty-six thousandths or

946/1000

• Math -

Remember that "percent" means "per hundred". So 94.6% means 94.6 per hundred, which is the same as

94.6
-----
100

Either use a calculator or move the decimal point 2 places to the left in the numerator. Either way, you get 0.946.

Reading the decimal, we get 946 thousandths. Or

946
-----
1000

We have to reduce that. Both the numerator and the denominator are divisible by 2. Dividing both by 2 we get

473
---
500

Now the problem is trying to figure out whether or not 473 has any factors at all, let alone any in common with 500. Using the rules of divisibility, we can see that 473 is not divisible by 2, 3, 4, 5, 6, 8, 9, or 10. Trying other numbers shows that 473 is not divisible by 7, but it is divisible by 11: 473 / 11 = 43. However, the only factors of 473 (11 and 43) are both prime, and neither goes into 500, so 473/500 is reduced.

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