Question Video: Finding the Percentage and the Part Knowing the Decimal and the Whole Mathematics

Video Transcript

If 0.05 is equal to 𝑎 percent, which is equal to 𝑏 over 20, find 𝑎 and 𝑏.

In the first part of this question, we need to express the decimal 0.05 as a percentage. We recall that any decimal 𝑑 can be written as a percentage 𝑝 percent by multiplying 𝑑 by 100. This means that in this question, 𝑎 is equal to 0.05 multiplied by 100. As multiplying by 100 moves all our digits two places to the left, 0.05 multiplied by 100 is five. 0.05 is equal to five percent. Therefore, 𝑎 is equal to five. We also need to write this decimal as a fraction. As 0.05 is equivalent to five hundredths, we have the fraction five over 100.

We’re asked to write this in the form 𝑏 over 20. Since 20 multiplied by five is 100, we’ve divided the denominator of our fraction by five. We must do the same to the numerator. And as five divided by five is equal to one, the fraction five hundredths is equivalent to one twentieth. And we can therefore conclude that 𝑏 is equal to one. The decimal 0.05 is equivalent to five percent and one twentieth as a fraction in its simplest form.