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Understanding Place Value

What is the value of the underlined digit?

Question 1.
a. 83,764 _______
60

Explanation:
We know that,
The place value is the value of a digit according to its position in the number such as,
ones, tens, hundreds, thousands, and so on.
So, the place value of 6 in 83,764 is 6 tens or 60.

b. 328.367 _______
0.007 or 7 thousandth.

Explanation:
We know that,
The place value is the value of a digit according to its position in the number such as,
ones, tens, hundreds, thousands, and so on.
But in decimal numbers,
the first digit after the decimal represents the tenths place, next digit represents the hundredths place and so on to fill in the place values until there are no digits left.
So, in the given number 7 in 328.367  is in thousandth place.

Write the digit that is in the given place value.

Question 2.
a. 32.376 – thousandths ____
6 thousandths.

Explanation:
We know that the place value is the value of a digit,
Face value is the actual value of the digit,
whereas place value is the position of a digit in a number.
From the given number 32.376, 6 is in the thousands place.
So, based on the above given chart,
the place value of 6 in 32.376 is written as 6 thousandths or 0.006.

b. 3,693.34 – hundreds ______
6 hundreds.

Explanation:
We know that the place value is the value of a digit,
Face value is the actual value of the digit,
whereas place value is the position of a digit in a number.
From the given number 3,693.34, 6 is in the hundreds place.
So, based on the above given chart,
the place value of 6 in 3,693.34 is written as 6 hundreds or 600.

Question 3.
a. 4.398 – hundredths _________
9 hundredths.

Explanation:
We know that, every digit in a number has a place value on the basis of its position in the number.
But in decimal numbers, the first digit after the decimal represents the tenths place, next digit represents the hundredths place and so on.
So, 9 is in the hundredths place of the given number 4.398.

b. 3,982.597 — tens _______
8 or 8 tens.

Explanation:
We know that the place value is the value of a digit,
Face value is the actual value of the digit,
whereas place value is the position of a digit in a number.
From the given number 3,982.597, 8 is in tens place.
So, based on the above given chart,
the place value of 8 in 3,982.597 is written as 8 tens or 80.

Convert these powers of ten to standard numbers.

Question 4.
a. 109 ____________
1,000,000,000

Explanation:
An exponent is a number that shows how many times a base number is to be used in multiplication.
A power of ten is an exponent where the base number is always 10.
109 = 10 × 10 × 10 × 10 x 10 x 10 x 10 x 10 x 10 = 1000,000,000
So, 109 is written as 1000,000,000.

b. 105 ____________
100,000

Explanation:
An exponent is a number that shows how many times a base number is to be used in multiplication.
A power of ten is an exponent where the base number is always 10.
105 = 10 × 10 × 10 × 10 x 10 = 100,000
So, 105 is written as 100,000.

Multiply or divide by the given power of ten.

Question 5.
a. 532.4 × 100 _____________
53,240

Explanation:
We know that,
when a number is multiplied by a multiple of 10,
the number of zeros and decimals in the product will vary based on the value of the multiple of 10 that is used and the decimal in the product moves to the right and zeros are added to the left of the decimal when needed.
So, 532.4 × 100 = 53,240

b. 12.22 ÷ 10 _______
1.222

Explanation:
We know that,
When a number is divided by a multiple of 10,
the number of zeros and decimals in the quotient will vary based on the value of the multiple of 10 that is used and the decimal in the quotient moves to the left and zeros are added to the right of the decimal when needed.
So, 12.22 ÷ 10 = 1.222

Question 6.
a. 4.412 × 1,000 ________________
4,412

Explanation:
We know that,
when a number is multiplied by a multiple of 10,
the number of zeros and decimals in the product will vary based on the value of the multiple of 10 that is used and the decimal in the product moves to the right and zeros are added to the left of the decimal when needed.
So, 4.412 × 1,000 = 4,412

b. 2,934.18 ÷ 100 _________
29.3418

Explanation:
We know that,
When a number is divided by a multiple of 10,
the number of zeros and decimals in the quotient will vary based on the value of the multiple of 10 that is used and the decimal in the quotient moves to the left and zeros are added to the right of the decimal when needed.
So, 2,934.18 ÷ 100 = 29.3418

Write the numbers below in expanded form.

Question 7.
a. 43.436 ________________
40 + 3 + 0.4 + 0.03 + 0.006

Explanation:
To write a decimal numbers in expanded form,
we need to break down each digit according to its place value.
First start with the whole numbers by identifying the place values of numbers as ones, tens, hundreds, thousands, and so on.
Then, move on to the decimal part as tenths, hundredths, and thousandths places.
So, 43.436 = 40 + 3 + 0.4 + 0.03 + 0.006

b. 3,682.3 _______
3,000 + 600 + 80 + 2 + 0.3

Explanation:
To write a decimal numbers in expanded form,
we need to break down each digit according to its place value.
First start with the whole numbers by identifying the place values of numbers as ones, tens, hundreds, thousands, and so on.
Then, move on to the decimal part as tenths, hundredths, and thousandths places.
So, 3,682.3 = 3,000 + 600 + 80 + 2 + 0.3

Compare each pair of decimals using <, >, or =.

Question 8.
a. 5.113 ____ 5.112
5.113 > 5.112

Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenths and hundredth place are same.
So, move to the thousandths place, the numbers are different.
Hence, 5.113 > 5.112 or 5.113 is greater than 5.112.

b. 42.882 ___ 43.88
42.882 < 43.88

Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenths and hundredth place are same.
So, move to the thousandths place, the numbers are different.
Hence, 42.882 < 43.88 or 42.882 is less than 43.88.

c. 4.6 ___ 4.600
4.6 = 4.600

Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenths are same.
In decimals if zeros are at the last, then there is no value.
So, 4.6 = 4.600

Question 9.
a. 7.295 ____ 72.95
7.295 < 72.95

Explanation:
Compare the whole number part first.
The numbers in tens place are different.
So, 7.295 < 72.95 or 7.295 is less than 72.95.

b. 23.54 ____ 23.45
23.54  > 23.45

Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenths are different.
So, 23.54  > 23.45 or 23.54  is greater than 23.45.

c. 9.563 ____ 9.653
9.563 < 9.653

Explanation:
Compare the whole number part first.
If the numbers are same, then go to the next number after the decimal.
The number in tenths are different.
So, 9.563 < 9.653 or 9.563 is less than 9.653.

Order the numbers from least to greatest.

Question 10.
5.6, 6.13, 5, 6.723
_____________
5, 5.6, 6.13, 6.723

Explanation:
Given,
5.6, 6.13, 5, 6.723
To order a group of decimals, line up the decimal points.
5.6,
6.13,
5,
6.723
All the ones are the same in 6.723 and 6.13 and have different tenths digit.
So, 6.723 is greater than 6.13
In the other two numbers when we compare the tenth place 5.6 is greater than 5.
Know list from least to greatest:
5, 5.6, 6.13, 6.723

Question 11.
75.931, 75, 74.2, 74.61
_____________
74.2, 74.61, 75, 75.931

Explanation:
Given,
75.931, 75, 74.2, 74.61
To order a group of decimals, line up the decimal points.
75.931,
75,
74.2,
74.61
All the ones and tens are same in 75.931 and 75 but have different tenths digit.
So, 75.931 is greater than 75.
In the other two numbers when we compare the tenth place 74.61 is greater than 74.2.
Know list from least to greatest:
74.2, 74.61, 75, 75.931

Question 12.
21.1, 20.5, 21.967, 20.35
_____________
20.35, 20.5, 21.1, 21.967

Explanation:
Given,
21.1, 20.5, 21.967, 20.35
To order a group of decimals, line up the decimal points.
21.1,
20.5,
21.967,
20.35
All the ones and tens are same in 21.967 and 21.1 but have different tenths digit.
So, 21.967 is greater than 21.1.
In the other two numbers when we compare the tenth place 20.5 is greater than 20.35.
Know list from least to greatest:
20.35, 20.5, 21.1, 21.967

Question 13.
47.85, 46.793, 47.7, 47.5
_____________
46.793, 47.5, 47.7, 47.85

Explanation:
Given,
47.85, 46.793, 47.7, 47.5
To order a group of decimals, line up the decimal points.
47.85,
46.793,
47.7,
47.5
All the ones and tens are same in 47.85 and 47.7 but have different tenths digit.
So, 47.85 is greater than 47.7.
In the other two numbers when we compare the ones place 47.5 is greater than 46.793.
Know list from least to greatest:
46.793, 47.5, 47.7, 47.85

Round each number to the indicated place.

Question 14.
a. 7.559 – ones
_____________
8

Explanation:
Round 7.559 to the nearest ones
Look at the tenths digit.
5 is greater than or equal to 5, so round 7 to 8 in the ones place.
Therefore, 7.559 is rounded to 8.

b. 2.165 – tenths
_____________
2.2

Explanation:
Round 2.165 to the nearest tenth.
Look at the hundredths digit.
6 is greater than 5, so round the number 1 to 2 in the tenths place.
Therefore, 2.165 is rounded to the nearest tenth as 2.2

c. 5.471 – hundredths
_____________
5.47

Explanation:
Round 5.471 to the nearest hundredth.
Look at the thousandths digit.
1 is less than 5, so 7 in the hundredth place remains same.
Therefore, 5.471 is rounded to the nearest hundredth as 5.47.

Question 15.
a. 3.337 – hundredths
_____________
3.34

Explanation:
Round 3.337 to the nearest hundredth.
Look at the thousandths digit.
7 is greater than 5, so round 3 to 4 in the hundredth place.
Therefore, 3.337 is rounded to the nearest hundredth as 3.34

b. 66.34 — ones
_____________
66

Explanation:
Round 66.34 to the nearest ones
Look at the tenths digit.
4 is less than 5, so 6 in the ones place remains same.
Therefore, 66.34 is rounded to 66.

c. 9.245 — tenths
_____________