Another Peek Beyond the Point | IT

Question 4

Can you give a simple rule to divide any number by a number of the form 1 followed by zeroes — 10, 100, 1000, etc.? For example, $\frac{123}{10}$ , $\frac{24}{100}$ or $\frac{678}{1000}$ ? Look for a pattern in the previous problems.

Solution

Dividing by 10, 100, or 1000 moves the decimal point left.

Step 1 — Dividing by 10

We will start with $\frac{123}{10}$ . The number 123 can be written as 123.0. We are dividing by 10, which has one zero. So, we move the decimal point one place to the left.

$123 \div 10$

$= 123.0 \div 10$

$\boxed{12.3}$

Diagram 1

Step 2 — Dividing by 100

Next, let us look at $\frac{24}{100}$ . The number 24 can be written as 24.0. We are dividing by 100, which has two zeroes. So, we move the decimal point two places to the left. We need to add a zero in front to make space.

$24 \div 100$

$= 24.0 \div 100$

$\boxed{0.24}$

Diagram 2

Step 3 — Dividing by 1000

Finally, let us consider $\frac{678}{1000}$ . The number 678 can be written as 678.0. We are dividing by 1000, which has three zeroes. So, we move the decimal point three places to the left.

$678 \div 1000$

$= 678.0 \div 1000$

$\boxed{0.678}$

Diagram 3

Step 4 — Discovering the rule

Let us look at our examples again. When we divided by 10, the decimal point moved one place left. When we divided by 100, the decimal point moved two places left. When we divided by 1000, the decimal point moved three places left. We can see a clear pattern here.

Answer

(i) To divide a number by 10, 100, 1000, etc., move the decimal point to the left. The number of places moved matches the number of zeroes in the divisor.

More questions in IT

Jonali and Pallabi play a game. Jonali says a fraction and Pallabi gives the equivalent decimal. Write Pallabi's answer in the blank spaces.

Jonali goes to the market to buy spices. She purchases 50 g of Cinnamon, 100 g of Cumin seeds, 25 g of Cardamom and 250 g of Pepper. Express each of the quantities in kilograms by writing them in terms of fractions as well as decimals.

Write the following fractions as a sum of fractions and also as decimals:

Can the product of two decimals be a natural number?

Can the product of a decimal and a natural number be a natural number?

Observe the number of digits after the decimal point in the multiplier, the multiplicand and the product. Also note the number of zeroes in the denominator.

Suppose we know that 596 × 248 = 147808, can you immediately write down the product of 5.96 × 24.8?

Context: Observe the number of digits after the decimal point in the multiplier, the multiplicand and the product. Also note the number of zeroes in the denominator.

Q. By looking at the above examples, can you frame a rule to multiply two decimals?

Q10

When is the product of two decimals greater than both the numbers? When is it less than both the numbers?

Q11

What is 0.039 m in centimetres and millimetres?

Q12

Complete the table by dividing the decimals:

Q13

Can you find the quotients of $10 \div 9$ , and $100 \div 11$ ?

Q14

Context: Let us consider the number 142857 that arose when dividing 1 by 7. Multiply 142857 by numbers from 1 to 6.

Q. What are the products? What do you notice?

Multiply 142857 by 7. What do you observe?

Q15

To find one such number, you can find $1 \div 17$ in decimal, and use the repeating block of digits.

Q16

Will the quotient be always greater than the dividend when the divisor is a decimal? Try it out with different values of the divisor.

Describe the relationship between the dividend, divisor, and the quotient. Create a table for capturing this relationship in different situations, like we did for multiplication.

Q17

What pattern do you observe? Why are 2 and 5 related in this way?

Q18

Do you know which month has this extra day?

Q19

With this new scheme of adding one extra day every 4th year, what is the number of days in 100 calendar years? Can you write an expression to calculate that number?

Q20

How many years are divisible by 4 in 100 years?

Q21

Can you form different expressions for the same question?

Q22

Context: The calendar designers decided that they will not add 1 extra day in every hundredth year.

Q. Can you write an expression for the number of days in 100 calendar years with this new adjustment?

Q23

With this final scheme of leap years can you calculate the number of calendar days in 10,000 years and the number of actual days the Earth will take to make 10,000 revolutions around the Sun? What is the difference? If there is a big difference, can you suggest a way to fix this problem?

Q24

Do you wonder how people figured out that the Earth completes one revolution around the Sun in exactly 364.2422 days?