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.
