The value of 0.18÷0.015 is:
100
Understanding Decimal Division: 0.18 ÷ 0.015
The problem asks us to find the value of the expression 0.18 divided by 0.015. This is a division problem involving decimals.
To divide one decimal number by another, it is often helpful to convert the divisor (the number we are dividing by) into a whole number. We can do this by multiplying both the numerator (the dividend) and the denominator (the divisor) by the same power of 10.
Step-by-Step Calculation of 0.18 ÷ 0.015
The expression is given as:
$\frac{0.18}{0.015}$
The divisor is 0.015. To make 0.015 a whole number, we need to move the decimal point 3 places to the right. This is equivalent to multiplying by $10^3$, which is 1000.
We must multiply both the numerator and the denominator by 1000 to keep the value of the fraction the same.
Multiply the numerator by 1000:
$0.18 \times 1000 = 180$
Multiply the denominator by 1000:
$0.015 \times 1000 = 15$
Now the division problem becomes dividing the new numerator by the new denominator:
$\frac{180}{15}$
Now we perform the division of 180 by 15.
We can do this by long division or by simplifying the fraction.
Let's perform the division:
$180 \div 15$
We can think:
- How many times does 15 go into 180?
- $15 \times 10 = 150$
- $180 - 150 = 30$
- How many times does 15 go into 30? $15 \times 2 = 30$
- So, $15 \times (10 + 2) = 15 \times 12 = 180$
Therefore, the value of $\frac{180}{15}$ is 12.
So, the value of $0.18 \div 0.015$ is 12.
Analyzing the Options
The given options are:
- 1/10
- 1/1000
- 10
- 100
The provided correct answer text is 100, which corresponds to Option 4.
Revision Table: Key Concepts in Decimal Division
| Concept | Description | Example |
|---|---|---|
| Dividend | The number being divided (numerator). | In 0.18 ÷ 0.015, the dividend is 0.18. |
| Divisor | The number by which the dividend is divided (denominator). | In 0.18 ÷ 0.015, the divisor is 0.015. |
| Quotient | The result of the division. | The quotient of 0.18 ÷ 0.015 is 12. |
| Multiplying by Power of 10 | Used to remove decimals from the divisor by shifting the decimal point. Must multiply both dividend and divisor by the same power of 10. | Multiplying 0.015 and 0.18 by 1000. |
Additional Information: Dividing Decimals
Dividing decimals is a fundamental arithmetic operation. A common method to simplify decimal division is to transform the problem into dividing whole numbers. This is achieved by ensuring the divisor becomes a whole number.
Steps for dividing decimals:
- Write the division as a fraction (dividend over divisor).
- Identify the divisor and count the number of decimal places it has.
- Multiply both the numerator (dividend) and the denominator (divisor) by the power of 10 that corresponds to the number of decimal places in the divisor (e.g., if 2 places, multiply by 100; if 3 places, multiply by 1000).
- This makes the divisor a whole number. The numerator will also become a whole number or a larger decimal.
- Perform the division using standard long division methods for whole numbers.
This technique helps avoid errors when placing the decimal point in the quotient, as it converts the problem into a more familiar format.
Important Questions from Simplification
Simplify √81 + ³√64 —————————— ³√3³ + 4² + ³√216
Simplify: 2×[4−{2−(2−3)−(2+3)}−1]−5×[−3−(3−2)]
Simplify: \((x^{\frac{m}{n}})^{m+n} \times (x^{\frac{n}{p}})^{n+p} \times (x^{p} \times x^{m})^{p-m}\)
Which of the following is correct for divisibility?
(A) A number is divisible by 6 if it is divisible by 3 or 2.
(B) A number is divisible by 5 if its unit digit is 0 or 5.
(C) A number is divisible by 3 if its unit digit is divisible by 3.
(D) A number is divisible by 4 if the number formed by its last two digits is divisible by 4.Choose the correct answer from the options given below:
The age of a father is thrice the age of his daughter. Ten years ago, his age was five times his daughter's age. Find the present age of the father.
