Decimal numbers: answer key to sixth grade exercises in PDF.

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1 The exercises in sixth corrected to download in PDF.

Answer key to 6th grade math exercises on decimal numbers. Exercises that deal with the integer and decimal part of a decimal number. The different writing and decomposition as well as the comparison.

Exercise 1:

Place spaces in the following numbers:
a. 1 512
b. 63 829
c. 468 803 576

Exercise 2:

a. In 13, the number of units is 3
b. In 692, the hundreds digit is 9
c. In 1,354, the tens digit is 5
d. In 6,083,472, the hundreds of thousands digit is 8.
e. In 7291, the number 9 represents the hundreds digit.
f. In 89 463 515, the number 9 represents the number of millions.

Exercise 3:

Calculate the following expressions:
A=(4×10)+2 = 40 + 2 = 42
B=(4×100)+(7×10) = 400 + 70 = 470 .
C=(3×100 000)+(6×10 000)+(1×10) = 360 010 .

Exercise 4:

Write each of the following numbers in figures:
a. forty-seven : 47
b. seven hundred and twenty-five: 725
c. two hundred and thirty-four thousand seven hundred and thirty-four: 234,734
d. ninety-six billion one hundred and eight million seven hundred and twenty-eight thousand thirty-two: 96,108,728,032 .

Exercise 5:

Convert the following data:
460 dm= 4,6 dam
8.3 dam = 8 300 cm
7,49 dam = 7 490 cm
80 mm = 0.000 8 hm
1 kL= 10 000 dL
13 cg= 0,13 g
400.1 g= 4.001 hg

Exercise 6:

Write in decimal form:
a. $\,3+\,\frac{1}{10}$ =3,1
b. $\,400\,+\,\frac{56}{10\,000}$ =400,0056
c. $\,3+\,\frac{6}{10}\,+\frac{2}{100}$ =3,62

Exercise 7:

Complete with two consecutive integers :
a. 6 6.2 7
b. 10 001 10,001.2 10 002
c. 3 940 3,939.01 3 939

Exercise 8:

a) Its integer part is 86 071 .

b) Its decimal part is 235 .

c) The number of thousandths is 5.

d) The number of units of thousands is 6 .

e) There are 86 thousand .

f) There are 3 hundredths.

g) There are 8 tens of thousands.

Exercise 9:

Consider the number 3 412 458.897 .

1) What is the tens, hundreds, hundredths digit?

The tens digit is 5, the hundreds digit is 4 and the hundredths digit is 9 .

2) What is the number of tens, hundreds, hundredths?

There are 341,245 tens, 34,124 hundreds and 89 hundredths.

3) Write this number in words.

Three million four hundred and twelve thousand four hundred and fifty-eight and eight hundred and ninety-seven thousandths .

4) Frame this number by two consecutive integers.

3 412 458 3 412 458.897 3 412 459

Exercise 10:

Exercise 11:

In each case, remove unnecessary zeros where possible.

$a.\,\,056$ = 56

$b.\,\,0103$ = 103

$c.\,\,062,0$ = 62

$d.\,\,15,170$ = 15,17

$e.\,\,603,04$ = 603,04

$f.\,\,010,010$ = 10,01

Exercise 12:

In each case, give a decimal of the

proposed number :

a. 2 tens 4 tenths 5 hundredths = 20.45 .

$b.\,(4\times \,1000)+(9\times \,10)+7+(9\times \,0,01)$ = 4097,09

$c.\,(5\times \,100000)+(6\times \,1000)+(7\times \,10)+(8\times \,0,1)$ = 506 070,8

$d.\,(9\times \,100)+5+(4\times \,0,01)+(2\times \,0,001)$ = 905,042

Exercise 13:

In each case, write the number and place a comma so that 5 is the number

hundredths of the number obtained.

a. 125 then 1.25

b. 335,000 then 3.35

c. 13,251 then 13,251

Exercise 14:

Find the decimal number whose :

– the number of tenths is 2 ;

– the tens digit is 3 ;

– the number of hundredths is 5 ;

– the number of units is 6 ;

– the number of thousandths is 9 .

The number you are looking for is 36 .259

Exercise 15:

In the writing of the number 621,345,

what is the number :

1. of the units is 1.

2. of the tenths is 3.

3. of the tens is 2.

4. hundreds 6.

Exercise 16:

Complete the following table:

Number	7,56	150,24	4,748	12,3
Tens digit	0	5	0	1
Number of tens	0	15	0	1
Number of hundredths	6	4	4	0
Number of tenths	5	2	7	3

Give the decimal form of each of the following numbers:

$3+\frac{8}{10}$ = 3,8

$12+\frac{53}{100}$ =12,53

$4+\frac{3}{10}+\frac{45}{100}$ =4,75

$12+\frac{9}{1000}+\frac{6}{10}$ = 12,609

Decompose the following decimal numbers according to the example below:

(For example: $15,48=1\times \,10+5\times \,1+\frac{4}{10}+\frac{8}{100}$ )

$3,4=3\times \,1+\frac{4}{10}$

$57,891=5\times \,10+7\times \,1+\frac{8}{10}+\frac{9}{100}+\frac{1}{1000}$

$10,002=1\times \,10+\frac{2}{1000}$

$362,07=3\times \,100+6\times \,10+2\times \,1+\frac{7}{100}$

Exercise 17:

For each question below, write the letter(s) corresponding to the correct answer (there may be several possible correct answers).

n°	Statements	A	B	C	D
1	4 is :	a number	a number	a letter	double of 8
2	The integer part of 25.08 is :	25,08	08	2508	25
3	The number 65…	… is an integer	… is a decimal number	…is not a whole number	…is not a decimal number

4	0260.020 equals:	260,2	26,02	260,02	26,2
5	The tens digit of 154.269 is :	1	2	5	15
6	56.02 is equal to :	$\frac{5602}{1000}$	${\color{DarkRed}\,\frac{5602}{100}}$	$\frac{56,02}{100}$
7	$\frac{60\,005}{100}$ is equal to :	6,05	65	60,005	600,05
8	$25+\frac{3}{100}+\frac{8}{1000}$ equals :	25,38	25,038	8325	25,308

Exercise 18:

Mario has written all the whole numbers from 1 to 100 in his notebook.

1) How many 1-digit numbers did Mario write? of 2-digit numbers?

He wrote 9 of them.

He wrote 90 of them.

2) How many numbers did Mario write in total?

Exercise 19:

Write the following numbers in decimal form:

$A=7\times ,100+4\times ,1+6\times ,0,1+2\times ,0,01$

${\color{DarkRed},A=704,62}$

$B=4\times ,10+5\times ,1+3\times ,0,01$

${\color{DarkRed},B=45,03}$

$C=\frac{7}{100}+\frac{3}{100}+\frac{7}{10}$

$C=0,{\color{DarkRed},}8$

Exercise 20:

1. Write the following numbers in figures:

seven million seven : 7,000,000,007 ;

eighteen units five thousandths: 18.005 ;

fifty three units and seventy five hundredths: 53.75;

three billion one hundred and five thousand and ten: 3 000 105 010.

2. Write the following numbers in words:

8,529,107 : eight million five hundred and twenty nine thousand one hundred and seven ;

15.017 : fifteen units and seventeen thousandths;

6,003: six thousand and three;

73.05 : seventy-three units and five hundredths;

508 : five hundred and eight .

Exercise 21:
a. Arrange in ascending order:

3,557< 5.3< 5,353< 35.35< 35.5 .

b. Arrange in descending order:

7.6> 7.25> 7.245 > 7.15 >7.05 .

Exercise 22:

What is the truncation to the unit (or integer part) of the following numbers?
397, 8 ; 5,02 ; 17,0 ; 449,9

The truncation of these numbers is: 397; 5; 17; 449.

Exercise 23:
a) 45 071
b) 3 700 500
c)203 107
d) 1235=1×1000 + 2×100+3×10+5
e) 24 103=2×10 000+4×1 000+1×100+3×1
f) 20 507 050=20×1 000 000+5×100 000+7×1 000 + 5×10

Exercise 24:

a. Four-billion-six-hundred-million years.
b. The length of the Rhone is eight hundred and twelve km.
c. Dinosaurs have been extinct for about sixty-five million years.

Exercise 25:

Exercise 26:
I am a 6-digit number and my integer part contains twice as many digits as my part
decimal point.

So there are 4 digits in the integer part and two in the decimal part.

My hundreds number is double the hundredths number.
My tenths number is the integer part of $\frac{527}{100}$ =5.27 .
so the number of tenths is 5.

My units number is the thousandths number of 0.2563.

The number of units is 6.

My hundredths number is the rounding to the unit of 4.38.
The number of hundredths is 4.
The number of hundreds is 8.

All my numbers are different and above 3.5.
The number is written -8 – 6.54

What is this number?
9876.54 or 7896.54
Exercise 27:

1. Arrange the following numbers in ascending order:

$24,139\,\,;\,\,24,56\,\,;\,\,25,1634\,\,;\,\,25,7\,\,;\,\,24,52.$

2. Arrange the following numbers in descending order:

$356,02\,\,;\,\,356\,\,;\,\,348,9\,\,;\,\,348,70\,\,;\,\,356,1005.$

Exercise 28:

A company needs to send a letter to two thousand three hundred and fifty-two customers.

She buys the envelopes in packages of one hundred.

How many packages of envelopes should she buy?

$\frac{2352}{100}=23,52$

Conclusion: she must buy 24 packages of envelopes.

Exercise 29:

The Bulgarian Stefka Kostadinova set the world record in high jump

in Rome in 1987 with a leap of 2m 09.

1. Express this jump in meters:

a. with a number in decimal writing.

2,09

b. with the sum of a whole number and a fractional writing.

$2+\frac{9}{100}$

Repeat question 1 with 1 m 96 which is the French high jump record

established by Maryse Ewanje-Epée in 1985.

1,96

and

$1+\frac{96}{100}$

Exercise 30:

Write the following numbers as decimals:

$a.\,\frac{524}{100}$ = 5,24

$b.\,\frac{2825}{1000}$ = 2,825

$c.\,\frac{9}{10}$ =0,9

$d.\,\frac{32}{10}$ = 3,2

$e.\,\frac{71}{100}$ =0,71

$f.\,\frac{5}{10000}$ = 0,000 5

Exercise 31:

Write in fractional form :

a. 5 tenths.

$\frac{5}{10}$

b. 27 hundredths.

$\frac{27}{100}$

c. 8 thousandths.

$\frac{8}{1000}$

d. 3 millionths.

$\frac{3}{1000000}$

Exercise 32:

Read and spell out each of the following numbers:

a.24

Ving-four

nine-cen- ving-seven-thousand-five-hundred-and-thirty-eight

nine-mile-thirty-four and one ten-thousandth.

six-thousand-two-four-twentieths

eighty thousand six hundred and twelve hundredths.

three hundred million and five-tenths.

The exercises in sixth corrected to download in PDF.

After having consulted the answers to this exercise on decimal numbers, you can return to the exercises in 6th grade.

The exercises in the sixth grade.

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