Without using a calculator, estimate 5785÷9.8 and then round your result up to the nearest 10.

Sure, let's break this down:

1. First, let's simplify the division to make it easier. We can round 9.8 up to 10 for simplicity. So now, we have 5785 ÷ 10.

2. Now, divide 5785 by 10. This is simple because dividing by 10 just means moving the decimal point one place to the left. So, 5785 ÷ 10 = 578.5

3. Finally, we need to round this result up to the nearest 10. The number 578.5 is between 570 and 580, but since we're rounding up, we'll round to 580.

So, the estimated result of 5785 ÷ 9.8, rounded up to the nearest 10, is approximately 580.