Sarin and the million numbers (Math Concept)

Standard

As an upper primary school student, Sarin has learnt numbers that count to millions as well as how numbers can be represented in decimal numbers, rounding off of numbers and the sequence of addition, subtraction, multiplication and division of numbers in mathematics questions. Sarin is delighted as now he knows how to manage the dollars and cents too.

Numbers

A number is formed by one digit or many digits.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A 7-digit number is a million number

A 8-digit number is a ten million number

The above number in word is Seventy five million, two hundred and sixty-six thousand, three hundred and eighty-two.

The digit ‘5’ stands for 5 millions or five million and the value of the digit is 5 000 000.

Ten thousand (10 000) less than 75 266 382 will give you a number 75 256 382 and in word is Seventy five million, two hundred and fifty-six thousand, three hundred and eighty-two.

75 266 382 round off to nearest hundred gives you number the 75 266 400.

75 266 382 round off to nearest thousand gives you number the 75 266 000.

Addition, subtraction, multiplication and division of numbers

Basic orders of calculation:

  1. Solve from left to right;
  2. Multiplication and division of numbers come 1st;
  3. If there are brackets, 1st solve everything in the brackets per the order in 1. and 2.

A. 4 198 + 5 × 21 – 18 ÷ 3

= 4 198 + 105 – 6

= 4 303 – 6

= 4 297

B. 4 198 + 5 × (21 – 18) ÷ 3

= 4 198 + 5 × 3 ÷ 3

= 4 198 + 15 ÷ 3

= 4 198 + 5

= 4 203

C. 4 198 + 5 × (21 – 18 ÷ 3)

= 4 198 + 5 × (21 – 6)

= 4 198 + 5 × 15

= 4 198 + 75

= 4 273

D. (4 198 + 5) × 21 – 18 ÷ 3

= 4 203 × 21 – 6

= 88 263 – 6

= 88 257

E. 4 198 + (5 × 21 – 18) ÷ 3

= 4 198 + (105 – 18) ÷ 3

= 4 198 + 87 ÷ 3

= 4 198 + 29

= 4 227

F. (4 198 + 5)× (21 – 18) ÷ 3

= 4 203 × 3 ÷ 3

= 12 609 ÷ 3

= 4 203

Decimal numbers

A number that cannot be divided in full and with remainder can be expressed as a decimal number.

Example:

126 ÷ 25 = 5 R 1 = 5 + 1/25 = 5 + 0.04 = 5.04

The answer 5.04 is a 2 decimal points number, the number round off to one-tenth or one decimal point will give number 5.0

A fraction or ratio can be expressed in decimal number and use for calculation or computing solution.

Example:

If Sarin has 5 apples and 6 oranges, the ratio of the apple to orange is 5 : 6

Ratio of apples to oranges = Number of apples : Number of oranges = 5 : 6

The normalized ratio reference to oranges = 5/6 : 6/6 = 0.8333 : 1

If you know the ratio of the apple to orange that Sarin has is 5:6. From the normalized ratio of 0.8333:1 you can determine how many apples or oranges he has.

If Sarin has 6 oranges, he will have 6 × 0.8333 ≈ 5 apples.

If Sarin has 100 oranges than he will have 100 × 0.8333 ≈ 83 apples

Interpret using mathematical model,

EbMNumber-2

Total number of orange in term of units = 6 units

Total number of apples in term of units = 5 units

If the quantities in 1 unit = 1

The number of oranges Sarin has is 6 group of 1 = 6 × 1 = 6

The number of apples Sarin has is 5 group of 1 = 5 × 1 = 5

If the total number of oranges Sarin has is 100

The quantities in 1 unit = 100 ÷ 6 = 16.7

Then the number of apples Sarin has is 5 groups of 16.67 = 5 × 16.7 ≈ 83

For number 75 256 382, can represented by decimal number as 75.256382 millions and the million is mathematics form is × 106.

75 256 382 = 75.256382 millions = 75.256382 × 106

It means,

75.256382 × 106

= 75.256382 × 1 000 000

= 75 256 382

Round off number 75 256 382 to nearest million or 106 will give 75 000 000 or 75 × 106 or 75 millions.

Dollars and Cents 

10 ten-cent coins make up to a dollar; if Sarin has 5 ten-cent coins that means he has 50 cents, or half a dollar in money value. In mathematical term, Sarin has 0.5 dollar or $0.50

The value of a dollar = $1 = 100 ₵

The value of 5 ten-cent coins = 5 × 10 = 50 ₵ = $50 ÷ 100 = $0.50

If Sarin has 12 ten-cent coins and 1 five-cent coin, he has 1.25 dollar or $1.25

The value of 12 ten-cent coins and 1 five-cent coin = 12 × 10 + 5 × 1 = 125 ₵ = $125/100 = $1.25

If Sarin has 50 ten-cent coins, Sarin has money in total value of 5 dollars. He cans exchange the coins to one five dollar note or five one dollar notes.

The value of a10-cent coin = 10 ÷ 100 = $0.10

The value of 50 ten-cent coins = 50 × 0.10 = $5.00

Singapore currency units

 Face Value Equivalent value example
1-cent coin
5-cent coin Five number of 1-cent coins
10-cent coin Two number of 5-cent coins
20-cent coin Two number of 10-cent coins
50-cent coin Five number of 10-cent coins
1-dollar coin Two number of 50-cent coins
1-dollar note Two number of 50-cent coins, or one number of 1-dollar coin
5-dollar note Five number of 1-dollar notes
10-dollar note Two number of 5-dollar notes
25-dollar note Five number of 5-dollar notes
100-dollar note Four number of 25-dollar notes
500-dollar note Five number of 100-dollar notes
1000-dollar note Two number of 500-dollar notes

USA currency units

 Face Value Equivalent value example
1-cent coin
5-cent coin Five number of 1-cent coins
a dime coin Two number of 5-cent coins
a quarter coin Five number of 5-cent coins
1-dollar note Four number of a quarter coins, or ten number of a dime coins
5-dollar note Five number of 1-dollar notes
10-dollar note Two number of 5-dollar notes
20-dollar note Four number of 5-dollar notes
100-dollar note Five number of 20-dollar notes
500-dollar note Five number of 100-dollar notes
1000-dollar note Two number of 500-dollar notes
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