Convert a Fractions to Decimals and Decimals to Percents (3/8, 7/4, 2 3/5)
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To complete the table, we will first write the
fractions as decimals, then write the decimals as percentages. Because a fraction bar means division, to convert a fraction to a decimal, we divide the numerator
by the denominator. So for the fractions
3/8, 3/8 is equivalent to three divided by eight. Let’s show the division on the right. Three eighths is equal to .375, however, we normally place a zero
on the one’s place value, and write the decimal as 0.375. Next we have the fraction 7/4. 7/4 is equivalent to
seven divided by four. Again, let’s show the
division on the right. 7/4 equals 1.75. For the last one notice
how we have a mixed number. We have two and 3/5. One option would be to
convert 3/5 to a decimal by dividing three by
five and then adding two, but let’s write the mixed
number as an improper fraction where the denominator remains five, and the numerator is five times
two plus three which is 13, and 13/5 is equivalent
to 13 divided by five. Again, let’s show the
division on the right. Two and 3/5 equals 2.6 as a decimal, and now let’s convert the
decimals to percentages. We will show two methods for doing this. For the first method, we
will write the decimal as a fraction, then if the denominator of the fraction is not 100,
we rewrite the fraction as a equivalent fraction
with the denominator of 100. This is important because
remember that percent is a number compared to
100, and then step three, we rewrite the ratio or fraction with a denominator of 100 as a percent. The second method is the
shortcut method in which we begin with the decimal, move
the decimal point two places to the right, and then add a percent sign. We will show both methods
for these three examples. Beginning with 0.375, we can write this as a fraction two ways. If we know our place values, we read this decimal as 375/1000. In this form, we need to
write a equivalent fraction with the denominator of 100, and because 1000 divided
by ten is equal to 100, we divide the numerator
and the denominator by ten. 375 divided by ten equals 37.5. 1000 divided by ten is equal to 100. Now that we have a fraction,
our ratio with a denominator of 100, the numerator
indicates the percentage. This is equal to 37.5%. Another way to write
0.375 as a fraction is to just write 0.375/1,
and now in this form, try an equivalent fraction
with a denominator of 100, we need to multiply the numerator and the denominator by 100. 0.375 times 100 is 37.5,
and of course one times 100 is equal to 100, giving us
the same result of 37.5%. So this is the percent. Let’s also take a look at
the shortcut method where I can bring the decimal to a percent. Beginning with the decimal,
the shortcut is to move the decimal point two places
to the right, so one two. The decimal point is now here, and then we add a percent sign, and of course we can now
remove the old decimal, and notice how this also gives us 37.5%. Now let’s look at the decimal 1.75. 1.75 is equivalent to one
and 75/100 using place value. Notice how the denominator is already 100, but we need to write the mixed number as an improper fraction to
determine the percentage. The denominator remains 100, and the numerator is 100 times
one plus 75, which is 175. Because the denominator is 100, the numerator indicates the percentage, this is equal to 175%, or another
way is to start with 1.75, and write the decimal as a
fraction with a denominator of one, and now to write
an equivalent fraction with a denominator of 100, we multiply the numerator and denominator by 100. 1.75 times 100 is equal to
175, one times 100 is equal to 100, giving us the
same percentage at 175%, and for the shortcut
method beginning with 175, move the decimal point two
places to the right, one two. The decimal point is now
here, add a percent sign. We can now remove the old decimal which of course also gives us 175%, and now let’s look at
the last decimal of 2.6. 2.6 is equal to two and 6/10. Now we right the mixed number
as an improper fraction, the denominator remains ten, the numerator is ten times
two plus six, which is 26. Now we write an equivalent fraction with the denominator of 100,
which means we now multiply the numerator and denominator by ten, because ten times ten is 100. 26 times ten is equal to
260, ten times ten is 100. Because we have a denominator of 100, the numerator indicates
this is equal to 260%, or we can also write
2.6 as a fraction with the denominator of one, and now to write an equivalent fraction
with the denominator of 100 we multiply the numerator
and denominator by 100. 2.6 times 100 is 260, one times
100 is 100, giving us 260%, and let’s show the shortcut one last time. Beginning with 2.6, move
the decimal point two places to the right, so one and two. The new decimal point is here. Notice how we are missing a digit here. We always replace
missing digits with zeros and then add a percent
sign, and of course now we can remove the old decimal point, which does give us 260%. I hope you found this helpful.

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