Question

Use numbers to explain the pattern you see when you count forward by tens.

Answer 1

Counting forward by tens reveals a pattern where the tens place increases by one while the ones place remains unchanged. This demonstrates the powers-of-ten notation in our decimal system, which allows for easy multiplication and division by simply moving the decimal point the number of places equal to the zeros in the power of ten.

Step-by-step explanation:

When we count forward by tens, we see a pattern in which the ones place stays the same and the tens place increases by one each time. For instance, starting from 10, counting forward looks like 20, 30, 40, and so on. This pattern occurs because every number is a multiple of 10, with the ones digit being 0.

This is directly connected to our powers-of-ten notation, where each position to the left is ten times bigger than the one to its right. This system originated from humans having ten fingers and using them to count. The usefulness of this system is evident in performing operations like multiplication and division with powers of ten. In such cases, we can simply move the decimal point instead of performing the operation in vertical format. For multiplication, we move the decimal point to the right by the count of zeros in the power of ten. Similarly, for division, we move it to the left.

For example, to multiply 123 by 10 (which is 101), we just move the decimal point one place to the right, resulting in 1230. Similarly, to divide by 100 (which is 102), we move the decimal point two places to the left in the number, which would convert 123 into 1.23.

Answer 2

If you can count from 1-10, then you can count forward by tens. You simply continue the pattern 1-10, but add a zero at the end: 1 2 3 4 5 6 7 8 9 10 becomes 10 20 30 40 50 60 70 80 90 100. When you continue past 100, the pattern repeats in the tens place, and eventually in the hundreds place: 110 120 130 140 150 160 170 180 190 200. And so on and so forth.