Math Problem Solver

$17.7857142857142$ rounded to $1$ significant figure is: $$2 \times 10^{1}$$ In scientific notation, and $$20$$ in standard notation.

Rounding a quantity to a given number of significant digits requires identifying the most significant digits of the quantity, which can be achieved by expressing the quantity in scientific notation. A quantity $q$ is said to be in scientific notation if $q = m \times 10^n$, where $1 \le \lvert m \rvert < 10$ and $n$ is an integer. The quantities $m$ and $10^n$ are called the mantissa and magnitude of $q$. Because the magnitude of the mantissa is between 1 and 10, the first digit of the mantissa is the most significant digit of the quantity $q$, the second digit of the mantissa is the second most significant digit of $q$, and so on.

Rounding $17.7857142857142$ to 1 significant figure can be achieved by expressing $17.7857142857142$ in scientific notation, and then rounding the mantissa to 1 significant figure. Since the magnitude of the mantissa is between 1 and 10, rounding the mantissa to 1 significant figure is equivalent to rounding it to the nearest $10^{1 - 1} = 10^{0}$. $$17.7857142857142 \approx 1.7 \times 10^{1}$$ $1.7$ rounded to the nearest $10^{0}$ is $2$. $17.7857142857142$ rounded to 1 significant figures is: $$2 \times 10^{1}$$