DECIMAL NUMBERS
Decimals are used in place of fractions. A fraction can be converted to a decimal and also a percentage, and Vice-Versa. In a decimal number there must be a dot which differentiates the Hundreds, tens, and units from the tenths, hundredths and thousandths.
Every number has its digits.
e.g 645 can be split into
600+40+5
(Hundred) +(Tens) + (units) .. This process is for whole numbers.
Take the first digit and multiply.
(6*100) + (4*10) + (5*1)
Decimals. If i add .345 to my number and made it 645.345
645. 345 will be represented
Hundred + Tens + Units . Tenths, Hundredths, Thousandths
(1/10) (1/100) (1/1000)
(3 * 1/10), (4* 1/100), (5*1/1000)
This is essentially what fractions is all about.
Every number has its digits.
e.g 645 can be split into
600+40+5
(Hundred) +(Tens) + (units) .. This process is for whole numbers.
Take the first digit and multiply.
(6*100) + (4*10) + (5*1)
Decimals. If i add .345 to my number and made it 645.345
645. 345 will be represented
Hundred + Tens + Units . Tenths, Hundredths, Thousandths
(1/10) (1/100) (1/1000)
(3 * 1/10), (4* 1/100), (5*1/1000)
This is essentially what fractions is all about.
Examples
1) Write down 40/100 as a decimal. (The whole number is less than 1, because the numerator is less than the denominator.) The denominator is 100 (Hundredths). Therefore it should be two decimal places. 40/100 = 0.40 (Because 4/1 = 4.)
Another way to divide to change to decimal numbers is by placing the decimal in front of 40. Then dividing by a hundredth. Now since the denominator is a hundredth with two zeros, move the decimal point two points to the left which gives you 0.40 Since it is a hundredth the number is less than one, and the only way this can happen is by reducing the value by shifting the point towards the left.
Another way to divide to change to decimal numbers is by placing the decimal in front of 40. Then dividing by a hundredth. Now since the denominator is a hundredth with two zeros, move the decimal point two points to the left which gives you 0.40 Since it is a hundredth the number is less than one, and the only way this can happen is by reducing the value by shifting the point towards the left.
2) Write down 0.25 in form of a fraction. (Numerator has to be smaller than the denominator)
This is two decimal places, therefore it is Hundredth.
Fraction = 25/100.
Another way to solve this is by making the .(dot a 1), and then add how many zeros depending on how many decimal places. 0.25 (2 decimal places), therefore 2 zeros which is a hundredth.
25/100 simplest form = 1/4
3) 12/100 + 5/1000 (Change this into decimal form)
First step: Both fractions need to have the same denominator.
Therefore 120/1000 + 5/1000 = 125/1000
Now change 125/1000 into a decimal
(Whole number should be less than Zero.) (There should be 3 decimal placing because it is thousandths)
125/1000 = 0.125
4) Write this in extended form (4.215)
This question is asking you to show the whole process of 4.215
4.215 =(4*1) +(2*1/10) +(1* 1/100) + 5* 1/1000).
This is two decimal places, therefore it is Hundredth.
Fraction = 25/100.
Another way to solve this is by making the .(dot a 1), and then add how many zeros depending on how many decimal places. 0.25 (2 decimal places), therefore 2 zeros which is a hundredth.
25/100 simplest form = 1/4
3) 12/100 + 5/1000 (Change this into decimal form)
First step: Both fractions need to have the same denominator.
Therefore 120/1000 + 5/1000 = 125/1000
Now change 125/1000 into a decimal
(Whole number should be less than Zero.) (There should be 3 decimal placing because it is thousandths)
125/1000 = 0.125
4) Write this in extended form (4.215)
This question is asking you to show the whole process of 4.215
4.215 =(4*1) +(2*1/10) +(1* 1/100) + 5* 1/1000).
Exercises
Complete the following
1) 6/10 + 4/100
2) 7+ 5/100
3) 16.854 (In expanded form)
4) 537.1 (In expanded form)
5) Which is smaller 0.15 Or 0.015
6) Which is bigger 2.117 or 2.1095
7) Arrange in ascending order: 3, 0.3, 0.03
8) Arrange in ascending order : 0.8, 1, 0.55
9) Write this fraction as a decimal (75/1000)
10) Write this fraction as a decimal (149/1000)
11) Write this fraction as a decimal (200/4000)
1) 6/10 + 4/100
2) 7+ 5/100
3) 16.854 (In expanded form)
4) 537.1 (In expanded form)
5) Which is smaller 0.15 Or 0.015
6) Which is bigger 2.117 or 2.1095
7) Arrange in ascending order: 3, 0.3, 0.03
8) Arrange in ascending order : 0.8, 1, 0.55
9) Write this fraction as a decimal (75/1000)
10) Write this fraction as a decimal (149/1000)
11) Write this fraction as a decimal (200/4000)