# Video: Solving Problems Involving Percentage

Estimate the following: 90% of 91.

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### Video Transcript

Estimate the following: 90 percent of 91.

In order to estimate an answer, we need to round our numbers to one significant figure. 90 percent is already rounded to one significant figure as it only has one nonzero digit. 91 rounded to one significant figure is equal to 90 as it is closer to 90 than one hundred. This is because the units digit one is less than five. The estimated calculation that we need to work out is 90 percent of 90.

There are lots of ways of answering this problem. One way would be to work out 10 percent first. To work out 10 percent of any number, we divide by 10. 90 divided by 10 is equal to nine. Therefore, 10 percent of 90 equals nine. We can therefore work out 90 percent by multiplying this answer by nine. Remember, whatever you do to one side of an equation, you must do to the other. Nine multiplied by nine is equal to 81. This means that 90 percent of 90 is equal to 81.

An alternative method of calculating 90 percent of 90 would be to turn our percent into a fraction or a decimal. 90 percent is equal to ninety hundredths as a fraction and 0.9 or 0.90 as a decimal. This is because the word percent means out of 100. The word of in maths means multiply. We can therefore multiply ninety hundredths or 0.9 by 90 to calculate 90 percent of 90. Once again both of these answers are equal to 81. When solving the fraction problem, we can cancel the zeros, which leaves us with nine multiplied by nine. This is equal to 81.

The calculation 0.9 multiplied by 90 can be rewritten as 0.9 multiplied by 10 multiplied by nine. 0.9 multiplied by 10 is equal to nine. And once again, we’re left with nine multiplied by nine, which is 81. We have therefore worked out using various methods that the estimate of 90 percent of 91 is equal to 81. We could work out the exact value by multiplying 0.9 by 91. This is equal to 81.9, which is very close to our estimated value.