Review of Place Values in Decimal Numbers
A decimal number includes a decimal point and digit(s) to the right
of the decimal point. Saying a decimal number aloud is very similar to
saying a whole number aloud.
How would you say the number 1375.2316 aloud? Once again,
you need to know the place values of the digits.
The place values of decimal numbers are related to the place values of
whole numbers. The whole number part (the part to the left of the decimal point)
has the same place values as before. What we’re interested in now are the
place values of the decimal part.
1 3 7 5 . 2 3 1 6
no th side
th side
Note how the place value names start from the decimal point. Going to the
left is ones, tens, hundreds, thousands, etc. as before. Going to the right
is tenths, hundredths, thousandths, ten-thousandths, etc.
The pattern going to the right or the left from the decimal point is the
same – but there are two big differences:
•The place values to the right of the decimal point all end in “th.”
•There is no such thing as “oneths.”
To say the number 1375.2316, say the whole number part, the word
“and,” (representing the decimal point), and the number to the right of the
decimal point, followed by the name of the place value of the last digit:
One thousand three hundred seventy-five and two thousand sixteen
ten-thousandths
1375 . 2016
name of place value of the 6
-------------------------------------------------------------------------------------------PRACTICE:
1) Name the digit in the following
places in the number 10,234.56789
a)
b)
c)
d)
e)
f)
2) Write the following numbers
in words.
tens
tenths
ten-thousands
thousandths
ones
hundredths
a)
b)
c)
d)
241.3
27.008
500.06
3.07021
3) Write the following numbers with digits:
a)
b)
c)
d)
six and nine tenths
one hundred two and three hundredths
twelve and three thousand two hundred forty-eight ten-thousandths
seven hundred six thousandths
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2
Rounding Decimal Numbers
Rounding with decimals is very similar to rounding with whole numbers.
As with whole numbers, you are asked to round a number to a given place value.
Everything to the right of the given place value becomes a zero, and the digit in
the given place value either stays the same or goes up one.
There is one big difference between rounding with decimals and rounding
with whole numbers. Zeroes at the end of a decimal number are dropped, while
zeroes at the end of a whole number must remain.
3600 ≠ 36
100,000 ≠ 1
36.00 = 36
1.00000 = 1
Dropping zeroes at the end of a whole
number changes the number.
Dropping zeroes at the end of a decimal
does not change the meaning.
One way to think of it is to consider the number “thirty-six dollars.” It can be
written equally well one of two ways:
$36 = $36.00
Any zero at the very end of a decimal number can be dropped:
18.25000 = 18.2500 = 18.250 = 18.25
Ex. 1.
A sprinter ran a race in 7.354 seconds. How long did the sprinter
take, rounded to the nearest tenth of a second? given place value
Go to the given place value and
look at the first digit to its right.
7.354
look here
3
Ex. 2.
If it’s greater than or equal to 5,
round up (increase the digit in the
given place value by 1). If it’s less
than 5, leave the digit in the given
place value alone.
7.354
Change all digits to right of the given
place value into zeroes. THIS IS AN
INTERMEDIATE STEP WHICH YOU
DON’T ACTUALLY WRITE DOWN.
7.400
Drop all zeroes at the end of the
decimal part.
7.4
5 = 5, so increase the 3 to a 4.
Final answer.
Round 7.354 to the nearest hundredth.
given place value
Go to the given place value and
look at the first digit to its right
7.354
If it’s less than 5, leave the digit
in the given place value alone.
7.354
look here
4 is less than 5, so leave 5 as is
Drop all zeroes to the right of the
given place value.
7.35
Sometimes you’re asked to round a decimal number to a place value
which is not in the decimal part.
Ex. 3.
Round 1,294.6374 to the nearest hundred.
given place value
Go to the given place value and
look at the first digit to its right
1,294.6374
9 is greater than or equal to 5,
so increase the 2 to a 3.
1,3_ _ . _ _ _
look here
4
Zeroes to the left of the decimal
must be included.
1,300. _ _ _
Zeroes to the right of the decimal
are dropped.
1,300
-------------------------------------------------------------------------------------------PRACTICE:
1) Round 62.15723 to the nearest
a)
b)
c)
d)
2) Round 1.608541 to the nearest
tenth
ten-thousandth
hundredth
thousandth
a)
b)
c)
d)
3) Round 17,289.3615 to the nearest
a)
b)
c)
d)
e)
f)
hundred-thousandth
thousandth
tenth
hundredth
4) Round 841.9508 to the nearest
ten
hundredth
thousand
one
tenth
thousandth
a)
b)
c)
d)
e)
f)
hundredth
one
tenth
ten
thousandth
hundred
--------------------------------------------------------------------------------------------
5
ANSWERS TO PRACTICE PROBLEMS
Page 2
1. a. 3
2. a.
b.
c.
d.
b. 5
c. 1
d. 7
e. 4
f. 6
two hundred forty-one and three tenths
twenty-seven and eight thousandths
five hundred and six hundredths
three and seven thousand twenty-one hundred-thousandths
3. a. 6.9
b. 102.03
c. 12.3248
d. .706
Page 3
1. a. 62.2
b. 62.1572
c. 62.16
d. 62.157
2. a. 1.60854
b. 1.609
c. 1.6
d. 1.61
3. a. 17,290
e. 17,289.4
b. 17,289.36
f. 17,289.362
c. 17,000
d. 17,289
4. a. 841.95
e. 841.951
b. 842
f. 800
c. 842.0
d. 840
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