Video: Decimals to Percentages

In this video, we will learn how to convert decimals to percentages for the rational system of numbers.

12:11

Video Transcript

In this video, we will look at how we convert decimals to percentages and vice versa. We will do this in a variety of situations. And we’ll begin by recalling some basic facts about decimals and percentages.

The word “percent” means out of 100. This means that 47 percent can be written as the fraction 47 over or out of 100. As the line in a fraction means divide, this is the same as 47 divided by 100. When dividing by 100, we move all the digits two places to the right. So 47 divided by 100 is equal to 0.47. We can, therefore, conclude that, in order to convert from a percentage, in this case 47 percent, to a decimal, 0.47, we divide by 100.

The opposite or inverse of dividing is multiplying. Therefore, to convert from a decimal into a percentage, we must multiply by 100. The decimal 0.36 can be converted into a percentage by multiplying it by 100. As multiplying by 100 moves all the digits two places to the left, 0.36 is the same as 36 percent.

We’ll now look at a couple of basic questions using this key rule.

Express 0.537 as a percentage.

We know that, in order to convert a percentage into a decimal, we need to divide by 100, as the word “percent” means out of 100. This means that, in order to convert from a decimal to a percentage, we need to multiply by 100, as multiplying is the inverse operation of dividing. In this question, we need to multiply 0.537 by 100. Multiplying by 10 moves all our digits one place to the left. So multiplying by 100 moves them two places to the left. 0.537 multiplied by 100 is 53.7. Our decimal expressed as a percentage is 53.7 percent.

This method can be used to convert any decimal into a percentage. We also recall that any decimal that has a zero in front of the decimal point will be less than 100 percent.

Write 7.5 as a percentage.

We recall here that one whole one, or 1.0, is equal to 100 percent. As 7.5 is greater than this, it will be greater than 100 percent. Seven or 7.0 must, therefore, be equal to 700 percent. We know that 0.5 is equal to a half, and a half of 100 percent is 50 percent. Adding these two values tells us that 7.5 written as a percentage is 750 percent.

An alternative method here would be to recall that to convert from a decimal to a percentage we need to multiply by 100. 7.5 multiplied by 100 is equal to 750, as all the digits move two places to the left. This confirms the correct answer of 750 percent.

Our next question involves using frequency tables to find percentages.

The given table shows the distribution of the number of foreign tourists, in millions, who visited a certain country in 2010 based on the nationalities. Using the frequency table, find the percentage of Russian tourists. Give your answer rounded to the nearest integer.

We need to calculate the percentage of Russian tourists. We can see from the table that there were 1.29 million Russian tourists. This was out of a total of 7.62 million tourists altogether. As both of these are in the same units, we can write the number of Russian tourists out of the total as a fraction, 1.29 over 7.62.

The line in a fraction means divide, and 1.29 divided by 7.62 gives us 0.169291 and so on. We need to convert this answer to a percentage. And to convert any decimal into a percentage, we multiply by 100. Multiplying any number by 100 moves all the digits two places to the left. So 0.169291 multiplied by 100 is 16.9291 and so on.

We were asked to round our answer to the nearest integer. This means that the nine in the tenths column is the deciding number. If the deciding number is five or greater, we round up. The percentage of Russian tourists to the nearest integer is 17 percent. If required, we could repeat this process for the French, German, British, and Italian tourists.

The next question we look at involves comparing fractions, decimals, and percentages.

Which of the following expresses a decimal between 0.35 and 0.95, its fraction in simplest form, and its percentage form?

Let’s firstly consider the two different decimals that we have, 0.4 and 0.45. Both of these do indeed lie between 0.35 and 0.95. In order to convert a decimal into a percentage, we multiply by 100. 0.4 multiplied by 100 is equal to 40, and 0.45 multiplied by 100 is equal to 45. Our digits moved two places to the left. This means that we can immediately rule out options (C), (D), and (E), as their decimals and percentages do not match.

Both option (A) and option (B) have the decimal 0.4 and the percentage 40 percent. This means that we have an equivalent percentage form. Our next step is to work out which of the fractions is written in simplest form. The word “percent” means out of 100. So 40 percent can be written as 40 out of or over 100. This suggests that option (B) might be the correct answer.

However, 40 over 100 is not in its simplest form, as both the numerator and denominator are divisible by 20. 40 divided by 20 is equal to two, and 100 divided by 20 is equal to five. This means that the decimal 0.4 and the percentage 40 percent written as a fraction in simplest form is two-fifths or two over five. The correct answer was option (A) 0.4, two-fifths, and 40 percent.

Our final question involves adding decimal numbers to fractions and getting the sum in percentage form.

Fill in the missing value. 0.51 plus nine twentieths is equal to blank percent.

Normally, with a question like this, we would look to turn both numbers into either decimals or fractions. However, as we’re looking to give our answer as a percentage, it is worth turning both of them into percentages first. We want to convert 0.51 and nine twentieths into percentages.

The word “percent” means out of 100. We, therefore, need to find an equivalent fraction to nine twentieths that is over 100. 20 multiplied by five is equal to 100. As we have multiplied the denominator by five, we need to multiply the numerator by five. Nine times five is equal to 45. As 45 over 100 is the same as 45 percent, then nine over 20 is also equal to 45 percent. To convert any decimal into a percentage, we need to multiply by 100. 0.51 multiplied by 100 is equal to 51. Therefore, this is equal to 51 percent.

Our calculation becomes 51 percent plus 45 percent. 51 plus 45 is equal to 96. Therefore, 0.51 plus nine twentieths is equal to 96 percent.

We will now look at some of the key points from this video. The word “percent” means out of 100. This means that any percentage can be written as a fraction out of 100. For example, 21 percent is equal to 21 out of 100. As the line in a fraction means divide, this is also equal to 0.21.

To convert from any percentage to a decimal, we divide the percentage by 100. The opposite or inverse of this is also true. To convert from a decimal to a percentage, we multiply by 100. This can be summarized on the diagram below. Any decimal that has a zero in front of the decimal point will be equal to a percentage less than 100. For example, 0.74 is equal to 74 percent, and 0.286 is equal to 28.6 percent. If we have a nonzero value in front of the decimal point, on the other hand, our percentage will be greater than 100. 4.3 is equal to 430 percent, and 6.28 is equal to 628 percent. This comes from the fact that one whole one, or 1.0, is equal to 100 percent.

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