﻿Teacher Sarah stands in a studio next to a large touchscreen. She has short brown hair and wears a blue shirt with a print that reads "Homework zone."

A chart appears on the large touchscreen. The columns read "Hundreds, tens, ones, decimal, tenths, hundredths, thousandths."

Sarah says HI, TVO KIDS.
I'M TEACHER SARAH.
AND TODAY WE'RE GOING TO TALK
NUMBERS BY POWERS OF TENTHS.
THAT JUST MEANS MULTIPLYING
DECIMALS BY TENTHS,
HUNDREDTHS AND THOUSANDTHS.
LET'S GET STARTED.
HERE WE HAVE OUR
ORIGINAL NUMBER.

She points at the number 4.2, written on the table as 4 in ones, point in decimal and 2 in tenths.

She says THIS NUMBER IS FOUR
AND TWO TENTHS.
NOW LET'S SAY I WANTED TO
MULTIPLY FOUR AND TWO TENTHS
BY ONE TENTH.
I'M GOING TO TEACH YOU
A VERY EASY TRICK.
ALL WE HAVE TO DO IS TAKE A
LOOK AT OUR POWERS OF TENTH
AND FIGURE OUT HOW MANY PLACES
THERE ARE
AFTER
THE DECIMAL.
LET'S TAKE A LOOK.
HERE, FOR ONE TENTH,
NOTICE I HAVE ONE PLACE
AFTER THE DECIMAL.
SO WHAT THAT MEANS IS NOW
I CAN JUST MOVE MY DECIMAL
ONE PLACE TO THE LEFT.
HERE WE GO.

On the original number she moves the decimal one place to the left, forming the number .42.

She says BY MOVING IT ONE
PLACE TO THE LEFT,
I GET A PRODUCT OF
FORTY-TWO HUNDREDTHS
OR ZERO DECIMAL FORTY-TWO.
SO NOW LET'S TAKE OUR
SAME ORIGINAL NUMBER,
FOUR AND TWO TENTHS, BUT
THIS TIME WE ARE GOING TO
MULTIPLY BY ONE HUNDREDTH.
SO THE SAME THING, WE
HAVE TO COUNT THE NUMBER
OF PLACES THAT OCCUR
AFTER THE DECIMAL.
HERE WE HAVE ONE AND TWO.
SO WHAT THAT MEANS IS THAT
NOW WE HAVE TO TAKE OUR
DECIMAL AND MOVE IT TWO
PLACES TO THE LEFT.
HERE WE GO.

As she moves the decimal two places to the left she says ONE... TWO.

She adds a zero and says AND FOUR AND TWO TENTHS
MULTIPLIED BY ONE HUNDREDTH IS
FORTY-TWO THOUSANDTHS OR
ZERO DECIMAL ZERO FOUR TWO.
NOW DON'T BE
ALARMED, TVO KIDS.
USUALLY WHEN WE'RE MULTIPLYING
OUR NUMBERS GET LARGER,
BUT IN THIS CASE WE'RE
MULTIPLYING BY NUMBERS
THAT ARE LESS THAN ONE
SO OUR PRODUCT IS
GOING TO GET SMALLER.
HAPPY MULTIPLYING!