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: \((x^{\frac{m}{n}})^{m+n} \times (x^{\frac{n}{p}})^{n+p} \times (x^{p} \times x^{m})^{p-m}\)
Simplify: 2×[4−{2−(2−3)−(2+3)}−1]−5×[−3−(3−2)]
Simplify √81 + ³√64 —————————— ³√3³ + 4² + ³√216
The mean of scores obtained by 50 students is found to be 79.5. Later on, it was found that the score of one student was read as 94 in place of 49 and the score of another student was read as 69 in place of 89. Find the correct mean.
Correct the following equation by interchanging the two signs: 4 × 2 + 6 ÷ 2 -12 = 2
