To decrease a given number by 30%, we need to find the factor by which the original number should be multiplied. Here's the step-by-step process to determine that factor:
1. Understanding Percentage Decrease:
- Decreasing a number by 30% means the number is reduced by 30% of its value.
- This implies that 70% of the original value remains (since [tex]\(100\% - 30\% = 70\%\)[/tex]).
2. Converting Percentage to Decimal:
- Percentages are often more conveniently used in decimal form for calculations.
- 70% in decimal form is [tex]\(0.70\)[/tex] (since [tex]\(70 \, \text{\%} = 70 \div 100 = 0.70\)[/tex]).
3. Determining the Multiplication Factor:
- Hence, to find the new value after a 30% decrease, the original number should be multiplied by [tex]\(0.70\)[/tex].
Therefore, the number by which a given number must be multiplied to decrease it by 30% is [tex]\(0.7\)[/tex].
