Question

carry out the indicated operation and give your answer with 2 significant digits. 282.13 ÷ 0.084 what is 282.13 ÷ 0.084 with two significant digits? (type an integer or a decimal.)

Explanation:

Step1: Perform the division

First, calculate \( 282.13 \div 0.084 \). Using a calculator, we get \( 282.13\div0.084\approx3358.690476 \).

Step2: Round to two significant digits

To round to two significant digits, we look at the first two non - zero digits. The number is approximately \( 3.4\times10^{3} \) (or 3400 when considering significant figures in the context of a whole number approximation here). Wait, actually, let's do it properly. The first significant digit is 3, the second is 3 (wait no, 3358.69... the first two significant digits are 3 and 4? Wait, no. Wait, 3358.69. The first significant digit is 3, the second is 3? Wait, no, significant digits are counted from the first non - zero digit. So 3358.69 has the first significant digit 3, second 3, third 5, etc. But we need two significant digits. So we round 3358.69 to two significant digits. The rule is that if the digit after the second significant digit is 5 or more, we round up the second significant digit. So 3358.69, the first two significant digits are 3 and 3? Wait, no, 3358.69 is 3.35869×10³. To two significant digits, we look at the third digit (5) which is more than 5, so we round the second significant digit (3) up to 4. So 3.4×10³ which is 3400. But wait, let's check the division again. \( 282.13\div0.084=\frac{282.13}{0.084}\approx3358.69 \). Rounding to two significant digits: the first significant digit is 3, the second is 3, the next digit is 5, so we round the second 3 up to 4. So the number is approximately 3400 when rounded to two significant digits. But in decimal form, if we consider it as a decimal, 3358.69 rounded to two significant digits is 3.4×10³ or 3400.

Answer:

3400